Method For Solution Of Problems Research Articles

Numerical Application of Higher Order Linear Block Method for Solving Some Fourth Order Initial Value Problems

The numerical application of higher order linear block method for the direct solution of fourth order initial value problems was proposed using the linear block algorithm, where the methods applied in block form. The method is zero-stabile, consistent and convergent when analyzing the properties of the method. The mathematical example solved using the method is effective, suitable, and acceptable for solving fourth order initial value problems. The method is also compared with existing work when solving similar systems of differential equation and obviously, the method performs better than those in literature and textual shown.

High-dimensional nonlinear Bayesian inference of poroelastic fields from pressure data

We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy measurements. To quantify posterior uncertainty, we adopt Markov Chain Monte Carlo (MCMC) approaches for generating samples. To increase the efficiency of these approaches in high-dimension, we make use of local information about gradient and Hessian of the target potential, also via Hamiltonian Monte Carlo (HMC). Our target application is inferring the field of soil permeability processing observations of pore pressure, using a nonlinear PDE poromechanics model for predicting pressure from permeability. We compare the performance of different sampling approaches in this and other settings. We also investigate the effect of dimensionality and non-gaussianity of distributions on the performance of different sampling methods.

Improved Runge-Kutta Method for Oscillatory Problem Solution Using Trigonometric Fitting Approach

This paper provides a four-stage Trigonometrically Fitted Improved Runge-Kutta (TFIRK4) method of four orders to solve oscillatory problems, which contains an oscillatory character in the solutions. Compared to the traditional Runge-Kutta method, the Improved Runge-Kutta (IRK) method is a natural two-step method requiring fewer steps. The suggested method extends the fourth-order Improved Runge-Kutta (IRK4) method with trigonometric calculations. This approach is intended to integrate problems with particular initial value problems (IVPs) using the set functions and for trigonometrically fitted. To improve the method's accuracy, the problem primary frequency is used. The novel method is more accurate than the conventional Runge-Kutta method and IRK4. Several test problems for the system of first-order ordinary differential equations carry out numerically to demonstrate the effectiveness of this approach. The computational studies show that the TFIRK4 approach is more efficient than the existing Runge-Kutta methods.

Explicit Runge–Kutta methods for the numerical solution of linear inhomogeneous IVPs

Runge–Kutta methods for the numerical solution of inhomogeneous linear initial value problems with constant coefficients are considered.A general procedure to construct explicit s-stage RK methods with order s, for the class of IVP under consideration, depending on the nodes ci,i=1,…,s is presented. This procedure only requires the solution of successive linear equations in the elements of the matrix A and avoids the solution of non linear equations.We obtain several RK schemes with number of stages s=5,…,8 and maximal order p=s for the class of problems under consideration. Finally, some numerical experiments to test the behaviour of the new RK schemes are presented.

A least-squares method for the numerical solution of a 2D optimal transportation problem

A least-squares method for the numerical solution of a 2D optimal transportation problem

A method for an approximate numerical solution of two-point boundary value problems: nonstandard finite difference method on a semi-open interval

A method for an approximate numerical solution of two-point boundary value problems: nonstandard finite difference method on a semi-open interval

A method for solution of a mixed boundary value problem for a hyperbolic type equation using the operators $\mathbb{AT}_{\lambda,j}$

A mixed boundary value problem with arbitrary continuous, not necessarily satisfying boundary conditions, functions in initial conditions and inhomogeneities of the equation is solved. A method is proposed for finding a generalized solution by a modification of the interpolation operators of functions constructed from solutions of Cauchy problems with second-order differential expression. Methods of finding the Fourier coefficients of auxiliary functions using the Stieltjes integral or the resolvent of the third-order Cauchy differential operator are proposed.

A method for an approximate numerical solution of two-point boundary value problems: nonstandard finite difference method on a semi-open interval

A method for an approximate numerical solution of two-point boundary value problems: nonstandard finite difference method on a semi-open interval

Communication-wise Comparison of the Online Resource Allocation Methods in CAV Fleets

Deploying fleets of Connected Autonomous Vehicles (CAVs), with limited peer-to-peer communication ranges, in order to provide On-demand Transport (ODT) services, requires a careful choice and evaluation of solution methods for resource allocation problems. We adopt in this paper a multiagent approach consists of: 1) defining a generic model to ODT's dynamic resource allocation problem in connected autonomous vehicle fleets, taking into account the limited connectivity and communication constraints, 2) behavior abstraction of AV Agents, and 3) abstracting the solution methods as Coordination Mechanisms (CMs) to define the characteristics of a solution method and its requirements to implement the corresponding planning sub-behavior. Using this methodology, we were able to compare the performance of a variety of solution methods with a set of evaluation criteria, namely for the solution Quality of Service (QoS) and Quality of Business (QoB). In this work, we focus on the communication-wise evaluation criteria, such as connectivity and network load.

Learning a simple multilayer perceptron with PSO

In this study, we attempt to learn the parameters of a multilayer perceptron (MLP) using the particle swarm optimization (PSO) method, which is an approximate solution method for optimization problems without requiring the derivative information of the evaluation function. We used the gradient method and PSO to learn to classify a linearly inseparable dataset with an MLP in the middle layer with a few neurons. We experimentally confirmed that PSO outperformed gradient-based learning.

Providing mechanisation of loading and unloading operations in hopper rail stores

Grain and fertiliser transportation are the fastest growing segments of the transportation services market, including railway transportation. Presidential Decree No. 204 of 7 May 2018 “On the national goals and strategic objectives for the development of the Russian Federation for the period until 2024” tasked the Russian government with developing a programme of measures to increase the productivity of economic sectors, including the agroindustrial complex. The increase in the productivity of the latter should entail the development of both domestic consumption and the export component, which places an additional burden on rail transport. The aim of the research is to improve loading and unloading operations in bunker-type railway yards by using auxiliary constructions to speed up and facilitate the loading and unloading of rolling stock by bulk cargo. The research is based on the principles of the system approach using methods of mathematical modelling of technical systems, numerical methods of problem solution and rheology engineering methods. The results of the research are resource-saving ways of bulk cargo loading and unloading from containers of various purposes, allowing to increase the degree of their uniform distribution in the container, and to ensure smooth release of material.

A Novel Two Point Optimal Derivative free Method for Numerical Solution of Nonlinear Algebraic, Transcendental Equations and Application Problems using Weight Function

It’s a big challenge for researchers to locate the root of nonlinear equations with minimum cost, lot of methods are already exist in literature to find root but their cost are very high In this regard we introduce a two-step fourth order method by using weight function. And proposed method is optimal and derivative free for solution of nonlinear algebraic and transcendental and application problems. MATLAB, Mathematica and Maple software are used to solve the convergence and numerical problems of proposed and their counterpart methods.

Transient response prediction of randomly excited vibro-impact systems via RBF neural networks

Systems exposed to random excitations may fail long before stationarity is achieved, which necessitates consideration of the transient responses of the system. On the other hand, the transient response prediction of non-smooth systems may face more obstacles than that of smooth systems. One of the foremost challenges lies in the handling of vector fields with singularities in non-smooth systems. In this work, the radial basis function neural networks (RBFNN) is utilized for the first time to analyze the transient response of randomly excited vibro-impact systems (VIS), a class of typical non-smooth systems. The solution of the system response is expressed in terms of a serious of Gaussian activation functions (GAFs) with time-dependent weights. These time-dependent weights are determined by minimizing a loss function, which involves the residual of the differential equations and constraint conditions. To avoid the singularity of the initial condition being a Dirac delta function, a strategy of short-time Gaussian approximation is presented to obtain the initial weights. Two typical VISs exposed to stochastic excitations are presented to verify the suggested scheme. Appropriate comparisons to the data obtained by digital simulation show that the method yields reliable results even for strongly nonlinear systems. With the merits of high computational accuracy and satisfactory efficiency, this approach is expected to be an effective method for solution of random vibration problems of high-dimensional complex non-smooth systems.

Kansa–RBF algorithms for elliptic BVPs in annular domains with mixed boundary conditions

We employ a Kansa–radial basis function (RBF) method for the numerical solution of elliptic boundary value problems in annular domains with mixed Dirichlet/Neumann boundary conditions. By exploiting the circular boundaries and the properties of circulant matrices we employ, in an efficient way, the pre-conditioned Krylov subspace iterative solvers GMRES and BiCGSTAB for the solution of the resulting linear systems. In particular, we employ block circulant pre-conditioners which allow for the efficient solution of the relevant systems in the iterative solution. Moreover, by exploiting the properties of circulant matrices we perform the matrix–vector multiplications involved in the iterative solvers efficiently. The feasibility of the proposed techniques is illustrated by several numerical examples.

Windowed Green function method for wave scattering by periodic arrays of 2D obstacles

AbstractThis paper introduces a novel boundary integral equation (BIE) method for the numerical solution of problems of planewave scattering by periodic line arrays of two‐dimensional penetrable obstacles. Our approach is built upon a direct BIE formulation that leverages the simplicity of the free‐space Green function but in turn entails evaluation of integrals over the unit‐cell boundaries. Such integrals are here treated via the window Green function method. The windowing approximation together with a finite‐rank operator correction—used to properly impose the Rayleigh radiation condition—yield a robust second‐kind BIE that produces superalgebraically convergent solutions throughout the spectrum, including at the challenging Rayleigh–Wood anomalies. The corrected windowed BIE can be discretized by means of off‐the‐shelf Nyström and boundary element methods, and it leads to linear systems suitable for iterative linear algebra solvers as well as standard fast matrix–vector product algorithms. A variety of numerical examples demonstrate the accuracy and robustness of the proposed methodology.

Optimizing borehole location for stress state assessment by geomechanical method of core discing

The article addresses the reliability of the stress–strain analysis and rockburst hazard assessment in rock mass using the geomechanical method of core discing. The theoretical experimentation used CAE Fidesys system. This system performs the strength and other-type computations using the finite element method—a numerical method of problem solution in applied physics. The experiments have two stages. At the first stage, the model of rock mass with core drilling for the stress state assessment by core discing is constructed; the computation aims to determine vertical stresses such that the tensile stresses along the core axis exceed the ultimate tension strength (discing condition). At the second stage, the rock mass with the destress boreholes is modeled; the aim of the modeling is to determine the influence zones of the destress boreholes. The applied experimentation was carried out in underground openings of Taimyrsky Mine. The research has found the influence exerted by some destress boreholes on the stress state assessment by core discing. The theoretical experiments and practical testing results show a good agreement, which proves their reliability. The final conclusions are: inside the protected zones formed by destress drilling, the stresses effectively reduce down to safe values; to avoid errors inrockburst hazard assessment by core discing, core drilling should be performed at a distance from the destressing surface not less than 5 diameters of the destress boreholes; interpretation of the stress state assessment results should take into account the nonuniform stress distribution in the plane of destressing. The authors appreciate participation of D. Kh. Gilyazev, Head of the Rockburst Prediction and Prevention Department, Taimyrsky Mine (till 2021) in this study.

Optimization Approaches for Multiple Conflicting Objectives in Sustainable Green Supply Chain Management

Over the years, the global supply chain has evolved into a more extensive interconnected complex network with multiple suppliers, manufacturers, and customers. Since environmental issues have become a burning question in recent years, the focus has shifted to attaining sustainability in supply chain management. The green supply chain or sustainable network is a concept to reduce environmental impacts in the life cycle of a product. However, green supply chain management is often challenged with additional operating costs and difficulty monitoring the implications within the complex network system. Additionally, many stakeholders are unaware of the importance of sustainability analysis, which eventually complicates adopting green cultures in actual applications. Since green supply chain management deals with multiple aspects, such as cost and carbon emission, the multiobjective optimization method is widely used to evaluate supply chain performance. This paper intensively reviews the state-of-the-art literature on applying multiobjective optimization techniques in green supply chain management. The study highlights aspects of green supply chain structures, model formulation techniques considering multiple objectives simultaneously, and solution methods for multiobjective optimization problems. Finally, a conclusion is drawn with the scope of the potential research opportunities for integrating economic and environmental considerations in sustainable supply chain management practice.

Development of an Order (k+3) Block-Hybrid Linear Multistep Method for the Direct Solution of General Second Order Initial Value Problems

Block hybrid linear multistep method was proposed to overcome the Dahl Quist order barrier for linear multistep methods. This research aims to answer questions relating to the convergence, accuracy, and effectiveness of the block hybrid method when utilized to obtain the solution of Initial Value Problems (IVPs). In this research, an order (k+3) block hybrid method applicable to obtain the direct solution of IVP’s of ordinary differential equations (ODEs) is presented. Collocation and interpolation of power series at finely selected grid points were used to improve the method’s consistency, convergence, accuracy and zero stability. Linear problems were solved to show the accuracy and efficiency of the proposed method, and the error obtained from the comparison of exact and approximate results shows that the proposed method is effective in solving the class of problem.

Language Policies Directed At Borchali and South Azerbaijan Turks and Mother Tongue Problem

Language is an important factor that constitutes national identity. Language policies have become a state structure that aims to unite peoples under state rule, as well as organize and reorganize their lives. The establishment of a political central authority that dominates the society’s thoughts through language is the most essential element of social construction processes in the new world order. This study examines the current situation of Azerbaijani Turkish in Borchali (Georgia) and South Azerbaijan (Iran) from socio-political and sociolinguistic perspectives. In this context, language policies, language planning and language rights, and monolingualism with its assimilationist characteristics, are included in the theoretical framework for the first part of this research. The second part explains the language policy implemented in Georgia and discusses the mother tongue education problems faced by minorities. Data on language policy practices in Iran, the position of Azerbaijani Turkish against the titular language, and the problems related to South Azerbaijan Turks’ right to education in their mother tongue are interpreted in the third part. In the last section, attention is drawn to the role of language policy in Azerbaijan’s multi-culturalism model, as a solution method for the aforementioned problems.

Optical Network Management by ONOS-Based SDN Controller

The possibilities to manage the optical network with a logically centralized SDN control plane based on the Open Network Operating System (ONOS) are investigated. The structure of the controller and its main functional blocks are considered ensuring the collection of information about the state of network elements, the solution of the main control tasks, interaction of control systems built on different technological bases, are considered. The role and place of the open network operating system in the controller structure are shown, the description of the ONOS multilevel architecture in the form of a set of functional modules is given, the purpose and functions of the ONOS subsystems are analyzed, protocols and interfaces making it possible to present the SDN network as a model are described. The peculiarity of the model is that the managed network can be represented as a set of virtual network functions. Therefore, the control process becomes independent of which vendor's equipment was used to build the network, as well as whether the network is built on real physical elements or virtual ones. Using the ONOS allows you to build a logical centralized control plane in the SDN networks. The existing set of functional modules, services and interfaces in the ONOS allows you to perform optical network management tasks. For the further development of the ONOS, it is necessary to develop mathematical models and methods for the optimal solution of control problems in various operating conditions, which will become application-level software modules in the future.