Mathematical Model Of Problem Research Articles

TWO-SIDED APPROXIMATIONS METHOD BASED ON THE GREEN’S FUNCTIONS USE FOR CONSTRUCTION OF A POSITIVE SOLUTION OF THE DIRICHLE PROBLEM FOR A SEMILINEAR ELLIPTIC EQUATION

Context. The question of constructing a method of two-sided approximations for finding a positive solution of the Dirichlet problem for a semilinear elliptic equation based on the use of the Green’s functions method is considered. The object of research is the first boundary value problem (the Dirichlet problem) for a second-order semilinear elliptic equation. 
 Objective. The purpose of the research is to develop a method of two-sided approximations for solving the Dirichlet problem for second-order semilinear elliptic equations based on the use of the Green’s functions method and to study its work in solving test problems.
 Method. Using the Green’s functions method, the initial first boundary value problem for a semilinear elliptic equation is replaced by the equivalent Hammerstein integral equation. The integral equation is represented in the form of a nonlinear operator equation with a heterotone operator and is considered in the space of continuous functions, which is semi-ordered using the cone of nonnegative functions. As a solution (generalized) of the boundary value problem, it was taken the solution of the equivalent integral equation. For a heterotone operator, a strongly invariant cone segment is found, the ends of which are the initial approximations for two iteration sequences. The first of these iterative sequences is monotonically increasing and approximates the desired solution to the boundary value problem from below, and the second is monotonically decreasing and approximates it from above. Conditions for the existence of a unique positive solution of the considered Dirichlet problem and two-sided convergence of successive approximations to it are given. General guidelines for constructing a strongly invariant cone segment are also given. The method developed has a simple computational implementation and a posteriori error estimate that is convenient for use in practice. 
 Results. The method developed was programmed and studied when solving test problems. The results of the computational experiment are illustrated with graphical and tabular informations.
 Conclusions. The experiments carried out have confirmed the efficiency and effectiveness of the developed method and make it possible to recommend it for practical use in solving problems of mathematical modeling of nonlinear processes. Prospects for further research may consist the development of two-sided methods for solving problems for systems of partial differential equations, partial differential equations of higher orders and nonstationary multidimensional problems, using semi-discrete methods (for example, the Rothe’s method of lines).

MODELING THE INFLUENCE OF THE STRUCTURE AND QUALITY OF ASSETS ON THE PROFITABILITY OF A COMMERCIAL BANK

In modern conditions, the methods of classical economic analysis are not enough to solve the problem of bank stability. This requires the development of methods and tools to analyze the current situation in the bank and to develop sound management decisions aimed at ensuring the stability of the bank. The article notes that the analysis of the influence of the structure and quality of assets on the profitability of commercial banks is an important step for assessing the financial position and reliability of a bank, and a method is proposed for constructing a model of the dependence of bank’s profitability on the factors that determine it. The scientific sources were the works of Russian and foreign researchers in the field of modeling and characteristics of the banking system, financial stability of credit institutions, assessment of the creditworthiness of potential borrowers, system organization and information technology. The article uses the methods of economic analysis, differential calculus and mathematical statistics, as well as the achievements of the main scientific schools dealing with the problems of economic and mathematical modeling and economic analysis of banking. In order to determine the most significant economic factors affecting the profitability of commercial banks, generalization of the theoretical, methodological and applied aspects of studies devoted to the study of the influence of the structure and quality of assets on the profitability of commercial banks was carried out, and a correlation and regression analysis was made. The model presented in the article can be used to predict changes in the profitability of Russian commercial banks and to predict promising directions for growth in profit and profitability of the bank.

ОПТИМИЗАЦИЯ ПАРАМЕТРОВ ВЕНТИЛЯТОРНЫХ УСТАНОВОК АППАРАТОВ ВОЗДУШНОГО ОХЛАЖДЕНИЯ ГАЗА

Purpose of the study. Optimization of the parameters of high speed fan units of air coolers, the combination of which achieves the highest economic efficiency of fan units and, accordingly, the most rational range of specific speed values for the modes of maximum efficiency of fan units in combination with the relative diameter of the sleeve. Development of a mathematical model for determining the local values of the parameters of the efficiency of highspeed fan installations. Sustainable development of territories with active subsoil use is closely related to solving the problems of improving industrial safety and the efficiency of cooling the compressed gas at compressor stations of main gas pipelines, which actualizes the problem of mathematical modeling of energy conversion processes in the impellers of fan units of gas air coolers (AVO) to increase the competitiveness of the oil and gas complex RF in the context of globalization. Research methods. To optimize and determine the limiting combination of calculated parameters, the mathematical method of searching for the area of local maxima of a multiparameter problem in this part was performed in two stages: a mathematical model was built for determining the local values of the parameters that ensure the highest efficiency of fan installations with high speed; the most rational limiting combination of design parameters was determined, at which the highest economic efficiency of fan installations is achieved. Research results. The possibility of increasing the economic efficiency of axial fan units of high speed, made according to aerodynamic schemes with one impeller for gas air cooling devices, has been established. Using the mathematical analysis of the basic laws of axial turbomachines, equations for the efficiency of a fan unit and a fan are obtained, depending on the specific speed. Formulas are obtained for the maximum values of the efficiency of the fan and the fan unit of various specific speed depending on the coefficient of the consumpconsumption speed and on the relative diameter of the impeller sleeve. A method is proposed for constructing aerodynamic schemes of axial fan units for air-cooled gas coolers of the "K" type with maximum maximum values of efficiency for given values of specific speed, relative diameter of the impeller sleeve, aerodynamic quality of the impeller profiles, coefficient of aerodynamic resistance of the flow path of the coefficient of flow velocity. The possibility of creating a fan installation with a speed of ny ≥ 400 with an efficiency of at least ηy=0,86. Application area. Enterprises of the oil and gas complex of the Russian Federation for cooling compressed gas using AVO compressor stations of main gas pipelines.

ПРОИЗВОДИТЕЛЬНОСТЬ СИЛ ТРАЛОВОЙ СИСТЕМЫ – II: ФИЗИЧЕСКОЕ МОДЕЛИРОВАНИЕ

The article is a continuation of scientific research and justification of the possibility of artificial intelligence technologies for the tasks of predictive modeling of the behavior of a trawl system in the process of fishing on a self-learning neural network. The definition of the productivity of forces is introduced - the second time derivative of the work of these forces. The intermediate result of the design of the trawl system is a project - an integrated set of characteristics described in a form suitable for its operation with a given performance of forces. To proceed to predictive modeling, it is necessary to determine the extent of similarity of the trawl system in different areas of its interaction. There is inter-discipline, which is manifested in the formulation of problems, in ap-proaches to their solution, in revealing the connections between theories, in the formation of new disciplines. Interdisciplinarity allows conducting research with the trawl system in its entirety, combining data from various disciplines (hydromechanics, electrodynamics, thermodynamics, acoustics, optics, etc.), leading to the emergence of new postulates and laws that synthesize the sci-entific knowledge necessary for a self-learning neural network of fishing for the trawl system. To combine the knowledge there was chosen the similarity theory as a mathematical modeling method based on the transition from ordinary physical quantities that affect the system being modeled to generalized complex-type quantities composed of original physical quantities, but in certain combinations, depending - from the specific nature of the process under study. The complex nature of these quantities has a deep physical meaning of reflecting the interaction of various influences. The similarity theory studies the methods of constructing and applying these variables and is used in cases of mathematical modeling when an analytical solution of mathematical modeling problems is impossible due to complexity and accuracy requirements. The similarity theory is used in these cases to synthesize relations obtained on the basis of the physical mechanism of the process under study and data of a numerical solution or experiment.

Using Rounding Errors in Modern Computer Technologies

Introduction. When solving problems of transcomputational complexity, the problem of evaluating the rounding error is relevant, since it can be dominant in evaluating the accuracy of solving the problem. The ways to reduce it are important, as are the reserves for optimizing the algorithms for solving the problem in terms of accuracy. In this case, you need to take into account the rounding-off rules and calculation modes. The article shows how the estimates of the rounding error can be used in modern computer technologies for solving problems of computational, applied mathematics, as well as information security. The purpose of the article is to draw the attention of the specialists in computational and applied mathematics to the need to take into account the rounding error when analyzing the quality of the approximate solution of problems. This is important for mathematical modeling problems, problems using Bigdata, digital signal and image processing, cybersecurity, and many others. The article demonstrates specific estimates of the rounding error for solving a number of problems: estimating the mathematical expectation, calculating the discrete Fourier transform, using multi-digit arithmetic and using the estimates of the rounding error in algorithms for solving computer steganography problems. The results. The estimates of the rounding error of the algorithms for solving the above-mentioned classes of problems are given for different rounding-off rules and for different calculation modes. For the problem of constructing computer steganography, the use of the estimates of the rounding error in computer technologies for solving problems of hidden information transfer is shown. Conclusions. Taking into account the rounding error is an important factor in assessing the accuracy of the approximate solution of problems of the complexity above average. Keywords: rounding error, computer technology, discrete Fourier transform, multi-digit arithmetic, computer steganography.

ON STABILIZATION PROBLEM FOR A LOADED HEAT EQUATION:THE TWO-DIMENSIONAL CASE

One of the important properties that characterize the behavior of solutions of boundary value problems for differential equations is stabilization, which has a direct relationship with the problems of controllability. The problems of solvability of stabilization problems of twodimensional loaded equations of parabolic type with the help of feedback control given on the boundary of the region are investigated in the article. These equations have numerous applications in the study of inverse problems for differential equations. The problem consists in the choice of boundary conditions (controls), so that the solution of the boundary value problem tends to a given stationary solution at a certain speed at t → ∞. This requires that the control is feedback, i.e. that it responds to unintended fluctuations in the system, suppressing the results of their impact on the stabilized solution. The spectral properties of the loaded two-dimensional Laplace operator, which are used to solve the initial stabilization problem, are also studied. The paper presents an algorithm for solving the stabilization problem, which consists of constructively implemented stages. The idea of reducing the stabilization problem for a parabolic equation by means of boundary controls to the solution of an auxiliary boundary value problem in the extended domain of independent variables belongs to A.V. Fursikov. At the same time, recently, the so-called loaded differential equations are actively used in problems of mathematical modeling and control of nonlocal dynamical systems.

Results of Application of Artificial Neural Networks in Predicting Geo-Mechanical Properties of Stabilised Clays—A Review

This study presents a literature review on the use of artificial neural networks in the prediction of geo-mechanical properties of stabilised clays. In this paper, the application of ANNs in a geotechnical analysis of clay stabilised with cement, lime, geopolymers and by-product cementitious materials has been evaluated. The chemical treatment of expansive clays will involve the development of optimum binder mix proportions or the improvement of a specific soil property using additives. These procedures often generate large data requiring regression analysis in order to correlate experimental data and model the performance of the soil in the field. These analyses involve large datasets and tedious mathematical procedures to correlate the variables and develop required models using traditional regression analysis. The findings from this study show that ANNs are becoming well known in dealing with the problem of mathematical modelling involving nonlinear functions due to their robust data analysis and correlation capabilities and have been successfully applied to the stabilisation of clays with high performance. The study also shows that the supervised ANN model is well adapted to dealing with stabilisation of clays with high performance as indicated by high R2 and low MAE, RMSE and MSE values. The Levenberg–Marquardt algorithm is effective in shortening the convergence time during model training.

Connecting mathematical modeling and social justice through problem posing

ABSTRACT This paper contributes to accumulating the knowledge base about prospective elementary school teachers’ (PTs’) understanding of socio-critical modeling by exploring how PTs make connections to features of mathematical modeling and social justice while posing mathematical problems and reflecting on their problem-posing. We present a conceptual framework for posing problems that connect social justice issues with the features of mathematical modeling. Drawing on the analysis of 36 individual modeling problems generated by the PTs and 36 written reflections PTs completed throughout their problem-posing activity, we illustrate various ways in which PTs connect the multi-faceted features of mathematical modeling (i.e., realistic context, model development, and shareable process) and social justice (i.e., micro – and macro – level). The PT-posed problems were categorized as (a) modeling problems presenting micro – and macro-level social justice issues (27%), (b) modeling problems presenting micro-level social justice issues (22%), (c) contextualized mathematical problems presenting micro – and macro-level social justice issues (25%), and (d) contextualized mathematical problems presenting micro-level social justice issues (17%). Our work describing the complexity of posing social justice-oriented mathematical modeling (SJMM) problems and articulating decisions PTs make while posing SJMM problems set directions for future efforts and research in teacher preparation.

Mathematical Models for Implementation of the Concept of Hard budget Restrictions in the budgetary system

The subject of the study is the processes of budget decentralization in the management of public finances, as well as mathematical methods and models for implementing the concept of hard budget restrictions in order to create conditions for the self-development of administrative-territorial units. The aim of the study is to develop adaptive economic and mathematical models for implementing the strategy of hard budget constraints implemented in the process of inter-budget regulation. The relevance of the study is due to the fact that currently the subject of acute discussion in the scientific community is the self-development of administrative-territorial entities and increasing their financial independence. In this regard, the focus of economic research is focused on the problems of budgetary decentralization as an engine of economic development, as well as the related topics of the use of mathematical tools for modeling decision support in this area. The created models are subject to the requirements of learnability, adaptability to changing conditions of environmental influences, and the ability to operate not only with quantitative, but also with qualitatively defined characteristics. The problem of mathematical modeling is solved by applying an interdisciplinary synthesis of the theories of stochastic automata operating in random environments and fuzzy logic. The proposed synthesis of theoretical and methodological devices is the novelty of the research. As a result , an economic and mathematical model of a fuzzy automaton is constructed for determining and quantifying the values of the norms for the distribution of tax revenues between budgets of different levels of the budget system. A fuzzy automaton interacts with a simulation model that reproduces budget flows and quantifies the decisions made by the automaton model. The practical significance of the research results lies in the program implementation of the developed models and their inclusion in the public finance management circuit. In the future , it is planned to create a mathematical model of the collective behavior of fuzzy automata models, the interaction of which solves the problem of coordinating the interests of budgets of different levels of the hierarchy in the distribution of tax revenues.

KONTRIBUSI KEMAMPUAN BERPIKIR KOMBINATORIK DALAM PEMBELAJARAN STATISTIKA MATEMATIKA

C ombinatoric ability allows the process of connecting several patterns and principles in formula discovery activities through generalizations to help students see the application of mathematics in real life. The model given can help in making broad rough estimates in developing their insights. The purpose of this study was to find out how combinatoric thinking skills are and whether combinatoric thinking skills contribute to mathematical statistics courses. This research belongs to the field of social sciences and can use this type of qualitative descriptive approach. The data were collected using a descriptive test which consisted of four items related to combinatoric problems. The data from the research results were processed using the SPSS program to get the contribution value of combinatoric thinking skills during the mid-test and final-test. with 23 students. The results of the analysis showed that the students' combinatoric thinking skills were quite good, where the mean and standard deviation were 71.27 and 6.09 during the middle exam and 72.00 and 5.88 at the time of the final exam. The problem that students have in combinatoric skills is the problem of mathematical modelling. The test results show that combinatoric thinking skills have a significant contribution to the mathematics-statistics course.

Mathematical modelling of the formation of small cell groups of invasive carcinoma

According to the latest research, cancer is a complex biosystem that develops in time and space. This means that cancer cells differ from each other in their function in the tumor. They are involved in various interactions in their microenvironment and compete for available nutrients for reproduction and survival. Identifying a specific structural type in the growth of a malignant tumor is one of the main problems today in oncology. The other no less important problem of mathematical modeling in oncology is the heterogeneity of a malignant neoplasm. In this work, we propose a chemomechanical model of the structure formation of small groups of cancer cells of invasive carcinoma of a non-special type (IC NST). The model suggests that carcinoma is a heterogeneous mass of cells of different phenotypes that perform different functions in the tumor. Each cell is represented by an elastic polygon that changes its shape and size as the tissue develops. Numerical modeling implements various subtypes of IC NST structures. The patterns are compared with morphological structures previously identified in clinical studies.

The program of the advanced training course for teachers of mathematics and informatics "Graphs and graph models: methods of visual processing "

The method of visual presentation of educational information for solving problems of mathematics and informatics is effective for the development of algorithmic, logical and computational thinking of schoolchildren. Technical progress, informatization of education, the emergence of modern software for visualization of information change the activities of teachers who need to master new technologies of information visualization for use in the classroom and in work with gifted children. Visual models for presenting educational information and methods of their processing with the use of computer programs are also relevant in extracurricular activities, allowing to develop the intellectual abilities of schoolchildren. Teachers are required to teach children to create projects in which visibility is a necessary component and must be represented by an electronic product created using modern information visualization tools. The article proposes a variant of the advanced training course for teachers of mathematics and informatics on teaching methods for visualization of solving problems using graphs and the free software “Graphoanalyzator”. The relevance of the course is due to the need to form the competency to carry out targeted work with gifted children in the use of software for creating and processing graphs based on the graph visualization program “Graphoanalyzator”. The authors believe that the training of teachers on this course will contribute to the formation of their skills to solve problems of mathematical modeling in informatics and mathematics, to apply information technologies to solve pedagogical problems in the context of informatization of education.

Mathematical Modeling of Invasive Carcinoma: Biomechanics of Small Groups of Cancer Cells

According to the latest research, cancer is a complex biological system that evolves over time and space. This means that cancer cells differ from each other in their functions in the tumor. They engage in various interactions with the microenvironment and compete for available nutrients to survive. The main problem of mathematical modeling in oncology today is the heterogeneity of a typical malignant neoplasm. In this work, we propose a chemomechanical model of the pattern formation of small groups of cancer cells of invasive carcinoma of a non-special type (IC NST). The model assumes that carcinoma is a heterogeneous formation, which consists of cells of different phenotypes performing different tasks to maintain the existence of the tumor. In the model, each cell is represented as a deformable polygon that changes its shape and size as the tissue develops. Numerical modeling implements various subtypes of IC NST structures. These patterns are compared with morphological structures identified in clinical studies.

The role of reading comprehension in mathematical modelling: improving the construction of a real-world model and interest in Germany and Taiwan

To solve mathematical modelling problems, students must translate real-world situations, which are typically presented in text form, into mathematical models. To complete the translation process, the problem-solver must first understand the real-world situation. Therefore, reading comprehension can be considered an essential part of solving modelling problems, and fostering reading comprehension might lead to better modelling competence. Further, ease of comprehension and involvement have been found to increase interest in the learning material, and thus, improving reading comprehension might also increase interest in modelling. The aims of this study were to (a) determine whether providing students with reading comprehension prompts would improve the modelling sub-competencies needed to construct a model of the real-world situation and their interest in modelling and (b) analyze the hypothesized effects in two different educational environments (Germany and Taiwan). We conducted an experimental study of 495 ninth graders (201 German and 294 Taiwanese students). The results unexpectedly revealed that providing reading comprehension prompts did not affect the construction of a real-world model. Further, providing reading comprehension prompts improved students’ situational interest. The effects of providing reading comprehension prompts on the construction of a real-world model were similar in Germany and Taiwan. Students’ interest in modelling improved more in Germany. An in-depth quantitative analysis of students’ responses to reading prompts, their solutions, and their interest in the experimental group confirmed the positive relation between reading comprehension and modelling and indicated that the reading comprehension prompts were not sufficient for improving reading comprehension. Implications for future research are discussed.

Aerodynamic Errors Mathematical Modeling in Air Data Systems Estimation Technology in Flight Tests Using Satellite Navigation Systems

Problems of mathematical modeling of onboard air data systems errors are of paramount importance in pitot-static sources errors determination, air data systems evaluation in flight tests. The problems of development, identification and assessment of the mathematical models of errors adequacy acquire main importance in the modern technology of the air parameters true values determination, air data systems evaluation using satellite navigation systems, developed and applied in the practice of flight tests at JSC "FRI n.a. M. M. Gromov". This paper gives a general description of an air data systems estimation technology using satellite navigation systems. The principles of solving problems of aircraft data systems aerodynamic errors mathematical modeling are stated. The structure of mathematical models, factors of the aerodynamic errors, relationship of the solving problems of errors modeling within the framework of technology with a flight experiment plan are shown. Mathematical models parameters identification are based on a complex solving of the problems of a true air data parameters values and aerodynamic errors determination in flight tests. New results of mathematical modeling of errors in tests at high angles of attack in 2018 year of medium-range and short-range aircraft are presented. The results illustrate the technology effectiveness in solving the problems of flight tests at high angles of attack information support, aerodynamic errors modeling, air data systems estimation. The applied modeling methods make it possible to allocate in the mathematical models of pitot-static sources aerodynamic errors even the factors of very weak aerodynamic influence, comparable with the minimum pressure sensors instrumental errors.

算数・数学教科書の問題から数学的モデリングの問題への 再教材化を目指した教員研修の可能性

算数・数学教科書の問題から数学的モデリングの問題への 再教材化を目指した教員研修の可能性

The Profiles of Students’ Problem Solving Abilities Visual Static Models in Mathematics

This study aims to determine the profile of the Mathematical Visual Static Model Problem Solving Ability. This study applies a qualitative approach by involving 8th-grade students at SMPN 1 Ajangale, who are selected from five different prototype groups and are based on students’ equations or mistakes in solving visual static model problems. Research subjects were selected during the data collection process from visual static model tests and interviews. The results showed that in completing the visual static model test, namely the first subject: overall good problem solving in knowledge skills, logical thinking, and mathematical logic, but did not have mathematical visualization and mathematical representation; for the second subject: mathematical representation, but lacks the ability of mathematical knowledge, logical thinking, mathematical understanding, visualization, and problem solving; for the third subject: mathematical knowledge skills, mathematical representation, mathematical understanding, problem solving, logical thinking, and mathematical visualization; for the fourth subject: logical thinking, but does not have mathematical understanding, mathematical knowledge skills, problem solving, mathematical representation, and mathematical visualization; and for the five subjects: logical thinking and mathematical representation, but lack of knowledge of mathematics, problem solving, mathematical understanding, and mathematical visualization.

Применение конечно-разностных моделей для краткосрочного прогнозирования природно-ресурсного потенциала

The article is about a problem of mathematical modeling of the natural resource potential of the Perm Territory by 1st and 2nd order finite-difference models. Such models can obtain better forecasts of complex socio-economic processes in comparison with the traditionally used linear multiple regression models. A high quality model of the natural resource potential with forecast possibi¬lities is one of the necessary conditions for the effective management of the natural resources of the region in order to ensure its sustainable economic development. Purpose of work. Aim of this work is work construction of finite-difference models of a natural resource potential complex indicators and an assessment of their prognostic properties. Materials and methods. Our research is based on Perm region statistical data for the period from 2001 to 2018. A multiple linear regression model is used as a comparison base. The natural resource potential complex indicator is calculated as a weighted sum of particular criteria characterizing the natural resources of the region. First and second order finite difference models are obtained by adding autoregressive terms of the first and second orders, respectively, to the multiple linear regression model. An estimation of the unknown parameters of the equations is carried out by a modified least squares method, which preserves the signs of the coefficients with the factors the same as in the original linear model. At the same time, the selection of explanatory factors and the assessment of the quality of the models are carried out based on the accuracy of the predicted values of the studied indicator. The results of the study. Components and factors of the natural resource potential is obtained, and a procedure for constructing finite-difference models is performed for three different time intervals: 2001–2018, 2001–2008, and 2008–2018. These intervals are chooseen because changes in the methodology for generating statistical data nearly 2008. Discussion and conclusions. The number of calculated predicted values was 18, and only in 4 out of 18 cases (22,2%) their quality is worse than forecasts obtained by the linear multiple model. So proposed modification of the multiple linear regression model with the addition of autoregressive terms makes it possible to improve the forecasting quality of the complex indicator of the natural resource potential of the region and, therefore, to make more effective decisions when managing its level.

Relevance of mathematical modelling of textile fillers’ 3-D structures for composite materials reinforcement

This paper discusses current and promising areas in the field of solving the fundamental problem of mathematical modelling in the design of bulk structures of textile fillers, which largely depend on the strength and weight characteristics of elements of aircraft made of polymer composite materials (PCM). Examples of mathematical modelling results of an aircraft engine blade’s textile filler for PCM are given. The study was funded by RFBR, project number 19-29-13044.

A metaheuristic approach for the comparative study of MHD flow of nano liquids in a semi-porous channel

In this paper, magneto-hydrodynamic flow of four different nanoliquids is presented. Two types of nanoparticles, viz. alumina and CuO are considered in water and ethylene glycol as base fluids. Appropriate models for nanoliquid physical properties are considered to incorporate the nanoparticle aggregation effects, nanoparticle shape, and size of the nanoparticles. Similarity transformations are used to convert the partial differential equations of the flow to nonlinear ordinary differential equations. The resultant system of equations is solved by Runge–Kutta finite difference method and an error function is designed which is optimized by using a metaheuristic algorithm, namely particle swarm optimization. The effect of flow parameters, viz. mass transfer parameter and Hartmann number and the nanoliquid parameters like nature of the base liquid, nanoparticle material, nanoparticle size, concentration of nanoparticle in base liquid on velocity distributions have been analyzed and discussed. The nanoparticle concentration and the particle size are found to have a significant role in the nanoliquid flow in the channel. The numerical results obtained from the proposed numerical method are validated with the previously published work under some special cases. The proposed numerical method holds excellent potential in mathematical modeling problems where the resultant equations are nonlinear coupled ordinary differential equations with unknown initial or boundary conditions.