Adomain Decomposition Research Articles

Significant statistical model of heat transfer rate in radiative Carreau tri-hybrid nanofluid with entropy analysis using response surface methodology used in solar aircraft

The recent advancement of technologies focuses on the use of solar-based heat radiation and nanotechnology. The primary source of heat is solar energy, which is obtained by absorbing sunlight. In addition, solar thermal planes, photovoltaic cells, and sun-based hybrid nanofluids all help to harness solar energy. Therefore, main concern of the study is to explored the two-dimensional Engine oil-based Carreau tri-hybrid nanofluid (SiO2 (silica dioxide), MOS2 (Molybdenum disulfide), Fe3O4(black iron oxide)) flow via a stretching sheet within solar wings. The flow phenomena of the non-Newtonian fluid enrich for the effects of radiant energy and the external heat source. By adopting similarity transfiguration, the dimensional partial main flow equations are changed into nonlinear dimensionless ordinary differential equations. The most effective and powerful tool of the semi-analytical method ADM (Adomain Decomposition Method) is utilized to solve the nanofluid flow problem. The uniqueness of the proposed study arises due to the analysis of entropy generation obtained by various irreversibility processes. The graphical illustration of outcome of various governing parameters on velocity, temperature, entropy terms and engineering quantities have been presented and theoretically analyzed. The findings reveal that The Carreau ternary hybrid nanofluids enhance the system's thermal conductivity for optimal temperature regulation in solar aircraft and better heat dissipation. The use of Carreau ternary hybrid nanofluids significantly reduces entropy generation, which implies a more reversible process, enhancing the overall efficiency of the energy conversion systems in solar aircraft. The heat flow of the system is accurately reflected by the chosen variables and their interactions, as demonstrated by the constructed model's strong statistical significance. For real-world applications, this improves the model's predictability and dependability.

Entropy analysis of Williamson fluid flow in a vertical porous channel with asymmetric cooling: Adomian decomposition method

AbstractThe paper presents the execution of the Adomian Decomposition Method to treat thermo‐fluidics of Williamson fluid flow in a vertical parallel plates channel filled with Williamson fluid–saturated porous medium. The channel walls experience asymmetric cooling. The fully developed flow setup constitutes a non‐linear boundary value problem tackled by the Adomain Decomposition Method (ADM) with the help of MAPLE. The computational procedure yields velocity, temperature distributions, skin friction, and Nusselt number. The results thus obtained are compared with those obtained by the RK‐Fehlberg numerical method to ascertain the accuracy of ADM. The results for quantities of interest viz. Skin friction. Nusselt number, entropy, and global entropy are shown in tabular/pictorial forms. These quantities exhibit qualitative and quantitative responses to embedded parameters discussed in detail in results and discussions section.

Analytical Solution of the Klein-Gordon coupled Equations via the Differential Transform Method

The basic equations in physical applications are the Klein-Gordon equation, as it gives a description of numerical particles in the fields of quantum and quantum mechanics, through the use of the differential transformation method and combining it with the Idomian method, in order to provide an integrated method for solving this equation, and it has been widely used to solve differential equations. Partial, to get rid of nonlinear terms and complex terms by integrating these two methods, which led to reducing the error and thus increasing the efficiency and accuracy of the solution using these numerical methods and the theoretical analysis of the method.. Researchers can learn more about quantum field dynamics using our method, which makes it easier to study a wide range of physical phenomena including scalar particles. In addition to improving the computational toolset in relativistic quantum mechanics, this work offers a useful foundation for investigating basic interactions in the field of particle physics and other fields. Conclusions: Adomain decomposition method (ADM) and the Differential Transform Method (DTM) together provide a powerful approach to solving the Klein-Gordon system equation. The effectiveness of this integrated method in efficiently and precisely solving complex differential equations controlling scalar particle dynamics has been proven by our research. The nonlinearities and boundaries of the Klein-Gordon system equation have proven to be formidable obstacles, but we have overcome them by combining the two approaches, and the findings are solid and trustworthy. Scalar particle behaviour in relativity quantum mechanics can be better understood with the help of this comprehensive methodology, which also improves computational efficiency. The DTM technique is a powerful and flexible tool for academics in many fields, including applied mathematics, particle physics, and quantum field theory, as our results show. The future looks bright for tackling ever more complex systems and improving our understanding of basic physical processes as we continue to investigate and enhance this integrated approach.

Existence and Numerical Investigation of Monkey-Pox Mathematical Model by Natural Adomain Decomposition Method

In this paper, studied the mathematical model concerning the transmission of Monkey-Pox disease. A class viral disease that mostly occurs in west and central Africa, transmitted from animals into human is belonging to the Small-pox family known is Monkey-pox infections disease. According to the scientist the primary best of the proposed disease is still in doubt. The proposed model will be investigate for the purpose of both qualitative and numerical solutions. At the early stage of this study, investigate the existence of proposed model. In this connection, the authors developed the desired condition of existence and stability for consider model by using the tools of analysis. At the second phase of this research work,the author investigated the numerical solutions for the consider Monkey-pox transmission diseases model. For numerical investigation, the authors use the tool of well know semi-analytical techniques known as Natural Transform coupled with Adomain Decomposition Method. The consider techniques are powerful tools for of obtaining approximate solutions of differential equation or system of differential equations. The proposed techniques base on recursive scheme for solutions of system of differential equations. For the authenticity and accuracy of obtain solutions, the obtain solutions are visualized graphically to desired the dynamical behavior of desired results with the help of Mathematica. That show the proposed method is best tools for solution of differential equations.

An implicit semi-analytical technique: Development, analysis and applications

Solving differential equations over extended temporal domains is pivotal for many scientific and engineering endeavors. The progression of numerous phenomena in the natural world occurs over prolonged durations, necessitating a comprehensive understanding of their temporal dynamics to facilitate precise prognostications and judicious decision-making. Existing methodologies such as homotopy perturbation, Adomian decomposition, and homotopy analysis are noted for their precision within limited temporal scopes. An optimized decomposition method proposed by Odibat extends this accuracy over a longer term, yet its solutions become untenable over substantial timeframes. This paper proposes a novel semi-analytical method to yield solutions over greater temporal extents. Moreover, this work integrates a convergence control parameter to bolster the proposed method’s accuracy and operational efficiency. A rigorous theoretical convergence analysis is delineated, substantiating the method’s validity. Three illustrative examples are numerically examined and discussed to validate the proposed approaches empirically.

New Gaussons and traveling wave solutions for fractional nonlinear logarithmic models

The principal objective of this paper is to remark upon an investigation on four kinds of fractional Schrödinger equations. New logarithmic fractional models are presented for two of these equations. While the other equations are just considered in their fractional cases. All models are solved by utilizing the Adomain decomposition method. By this method some new Gaussian soliton wave solutions and traveling wave solutions are obtained.

Triangular intuitionistic fuzzy linear system of equations with applications: an analytical approach

This study extended an existing semi-analytical technique, the Homotopy Perturbation Method, to the Block Homotopy Modified Perturbation Method by solving two n × n crisp triangular intuitionistic fuzzy (TIF) systems of linear equations. In the original system, the coefficient matrix is considered as real crisp, while the unknown variable vector and right hand side vector are regarded as triangular intuitionistic fuzzy numbers. The Block Homotopy Modified Perturbation Method is found to be efficient and practical to solve n × n TIF linear systems as it only requires the non-singularity of the n × n TIF linear system's coefficient matrix, whereas the point Homotopy Perturbation Method and other classical numerical iterative methods typically require non-zero diagonal entries in the coefficient matrix. A set of theorems relevant to this study are presented and demonstrated. We solve an engineering application, i.e. a current flow circuit problem that is represented in terms of a triangular intuitionistic fuzzy environment, using the suggested method. The unknown current is then obtained as a triangle intuitionistic fuzzy number. The proposed semi-analytic method is used to solve some numerical test problems in order to validate their performance and efficiency in comparison to other existing techniques. The numerical results of the example are displayed on graphs with different degrees of uncertainty. The efficiency and accuracy of the proposed method are further demonstrated by comparisons to block Jacobi, Adomain Decomposition method, Successive Over-Relaxation method and the classical Gauss-Seidel numerical method.

Utilization of Adomain Decomposition Method and Laplace Transform to Study Fractional KdV and Fractional Benjamin Models via Caputo Fractional Operator

Utilization of Adomain Decomposition Method and Laplace Transform to Study Fractional KdV and Fractional Benjamin Models via Caputo Fractional Operator

Numerical treatment for time fractional order phytoplankton-toxic phytoplankton-zooplankton system

<abstract><p>The study of time-fractional problems with derivatives in terms of Caputo is a recent area of study in biological models. In this article, fractional differential equations with phytoplankton-toxic phytoplankton-zooplankton (PTPZ) system were solved using the Laplace transform method (LTM), the Adomain decomposition method (ADM), and the differential transform method (DTM). This study demonstrates the good agreement between the results produced by using the specified computational techniques. The numerical results displayed as graphs demonstrate the accuracy of the computational methods. The approaches that have been established are thus quite relevant and suitable for solving nonlinear fractional models. Meanwhile, the impact of changing the fractional order of a time derivative and time $ t $ on populations of phytoplankton, toxic-phytoplankton, and zooplankton has been examined using graphical representations. Furthermore, the stability analysis of the LTM approach has been discussed.</p></abstract>

Solution and dynamics analysis of fractal-fractional multi-scroll Chen chaotic system based on Adomain decomposition method

In recent years, newly proposed fractal-fractional calculus operators have been used to predict the chaotic behavior of some attractors, and the new operators can capture self-similarity in the studied chaotic attractors. The results of varying with fractal order and fractional order are interesting, however, the dynamics are barely analyzed in these studies, and the law of fractal order and fractional order on the system is not clear. In this paper, the fractal-fractional differential operators with inverse operator property are redefined in the Caputo sense, and a new numerical scheme is proposed based on the sixth-order Adomain decomposition method. Then the dynamics of the new multi-scroll Chen chaotic system and its three degradation modes are analyzed completely in the fractal-fractional sense. The influence of the change of fractal order and fractional order on the chaotic system is revealed. Finally, a new physical phenomenon of the fractal-fractional chaotic system is captured by observing the coexistence of multi-scroll and two-scroll chaotic attractors of the new system through a wood-grain-like attractor basin, as well as transient chaos, chaotic jumps, and complex state transition behaviors. It is shown that fractal-fractional multi-scroll Chen system has complex and specific dynamical behaviors.

Dynamic Analysis and FPGA Implementation of a New Fractional-Order Hopfield Neural Network System under Electromagnetic Radiation.

Fractional calculus research indicates that, within the field of neural networks, fractional-order systems more accurately simulate the temporal memory effects present in the human brain. Therefore, it is worthwhile to conduct an in-depth investigation into the complex dynamics of fractional-order neural networks compared to integer-order models. In this paper, we propose a magnetically controlled, memristor-based, fractional-order chaotic system under electromagnetic radiation, utilizing the Hopfield neural network (HNN) model with four neurons as the foundation. The proposed system is solved by using the Adomain decomposition method (ADM). Then, through dynamic simulations of the internal parameters of the system, rich dynamic behaviors are found, such as chaos, quasiperiodicity, direction-controllable multi-scroll, and the emergence of analogous symmetric dynamic behaviors in the system as the radiation parameters are altered, with the order remaining constant. Finally, we implement the proposed new fractional-order HNN system on a field-programmable gate array (FPGA). The experimental results show the feasibility of the theoretical analysis.

Suggested Approach to Solve Nonlinear Ordinary Differential Equations

In this research a suggested method has been proposed to solve the non-linear ordinary differential equations, This method is somewhat similar to the Adomain decomposition method of solving equations but it is quite different in the using steps to find the non-linear boundaries , in the suggested method does not use an unknown parameter to calculate non-linear boundaries as well as the steps used to calculate non-linear boundaries are very simple and do not need many and complex steps. we can be called this approach by Fatima style to solve nonlinear ODE.

Dynamic efficacy of soil pollution using Fractional order model-An Adomian Decomposition approach

In this paper, a nonlinear fractional order eco-epidemic model of soil pollution is considered with four compartments namely, Susceptible soil (S), Polluted soil (P), Remediate soil (T) and Recovered soil (R). The local and global stability of both pollution free equilibrium and pollution extinction equilibrium points are studied around the equilibrium points. Also, the non-negativity and existence of unique solution of the model is proved using fixed point theorem. Adomain decomposition method is used to find the approximate solution of the proposed model. Numerical simulations of the model are carried out through MATLAB which helps to understand the role of parameters and to validate the theoretical findings.

A 〖(2n+9)〗^thDegree Polynomial Approximation Method for Solving Eight Order Linear Boundary Value Problems

Galerking method, Collocation method and least squired method have been used for solving boundary value problems (BVPs) and from practical point of view almost any success of above mention method depends on the selection of basis functions. Also, Adomain decomposition and variational iteration methods have been applied for the solution of BVPs and required respectively calculating the Adomian’s polynomials and Lagrange multipliers. In this paper a simple method of Degree polynomial approximation solution were n is number of successive derivatives of the governing equation is suggested as an alternative of the above mentioned methods. The method consists of first obtaining from the governing equation its n successive derivatives and boundary conditions a linear differential system of equations evaluated at the boundary points. Next, an approximate solution in the form of polynomial of degree with unknown coefficients is assumed. To determine the unknown coefficients, the assumed solution is incorporate into the linear differential system which turns to be a linear system of equation with unknowns which is salvable uniquely. The method is tested for n=5 to four examples. It clear that from tables 3.1 to 3.4 and figures 3.1 to 3.4 the numerical outcomes agree with the exact solution and also better than some existing results in the literatures. it should be also noted that the accuracy of the method can be increased by increased n. All Numerical computation were performed using maple 2016 software.

New Numerical Results on Existence of Volterra–Fredholm Integral Equation of Nonlinear Boundary Integro-Differential Type

Symmetry is presented in many works involving differential and integral equations. Whenever a human is involved in the design of an integral equation, they naturally tend to opt for symmetric features. The most common examples are the Green functions and linguistic kernels that are often designed symmetrically and regularly distributed over the universe of discourse. In the current study, the authors report a study on boundary value problem (BVP) for a nonlinear integro Volterra–Fredholm integral equation with variable coefficients and show the existence of solution by applying some fixed-point theorems. The authors employ various numerical common approaches as the homotopy analysis methodology established by Liao and the modified Adomain decomposition technique to produce a numerical approximate solution, then graphical depiction reveals that both methods are most effective and convenient. In this regard, the authors address the requirements that ensure the existence and uniqueness of the solution for various variations of nonlinearity power. The authors also show numerical examples of how to apply our primary theorems and test the convergence and validity of our suggested approach.

Qualitative properties and approximate solutions of thermostat fractional dynamics system via a nonsingular kernel operator

PurposeThis paper aims to study qualitative properties and approximate solutions of a thermostat dynamics system with three-point boundary value conditions involving a nonsingular kernel operator which is called Atangana-Baleanu-Caputo (ABC) derivative for the first time. The results of the existence and uniqueness of the solution for such a system are investigated with minimum hypotheses by employing Banach and Schauder's fixed point theorems. Furthermore, Ulam-Hyers (UH) stability, Ulam-Hyers-Rassias UHR stability and their generalizations are discussed by using some topics concerning the nonlinear functional analysis. An efficiency of Adomian decomposition method (ADM) is established in order to estimate approximate solutions of our problem and convergence theorem is proved. Finally, four examples are exhibited to illustrate the validity of the theoretical and numerical results.Design/methodology/approachThis paper considered theoretical and numerical methodologies.FindingsThis paper contains the following findings: (1) Thermostat fractional dynamics system is studied under ABC operator. (2) Qualitative properties such as existence, uniqueness and Ulam–Hyers–Rassias stability are established by fixed point theorems and nonlinear analysis topics. (3) Approximate solution of the problem is investigated by Adomain decomposition method. (4) Convergence analysis of ADM is proved. (5) Examples are provided to illustrate theoretical and numerical results. (6) Numerical results are compared with exact solution in tables and figures.Originality/valueThe novelty and contributions of this paper is to use a nonsingular kernel operator for the first time in order to study the qualitative properties and approximate solution of a thermostat dynamics system.

Solutions for some integral equations by variation iteration adomain decomposition method

The major aim of this work is to propose a novel method, the Variation Iteration Adomain Decomposition Method (VIADM), an iterative semi-analytical method to achieve an approximate analytical solution for nonlinear (Volterra / Fredholm) integral equations. This technique depends on applying the Adomain Decomposition Method (ADM) to a nonlinear term that can be solved using Adomain polynomials. The VIADM has been used to break down the Volterra integral equation solution into infinite components. Furthermore, some illustrative examples are given, and the results obtained indicate the proposed method’s accuracy, efficiency, and reliability.

Adomain Decomposition Method for Solving Integro-Differentional Equations of Fractional orders

في هذا البحث، سنقوم بدراسة نوع محور من المعادلات التفاضلية التكاملية ذات الرتبالكسرية بالشكل :حيث إن رتبة التفاضل والتكامل الكسريين تكون مختلفة ،حيث تم استخدام طريقة تحليلأدومن لحل هكذا نوع من المشاكل ولكلتا الحالتين الخطية وغير الخطية ، حيث ان هذا النوعمن المشاكل تكون من الصعب ايجاد حل لها بالطرق الاخرى.

A new fractional-order chaos system of Hopfield neural network and its application in image encryption

In this work, we propose a new fractional-order chaotic system based on the model of 4-neurons-based Hopfield Neural Network (HNN). By using Adomain decomposition method, the proposed fractional-order chaotic system is solved. With the orders changing, the proposed fractional-order system shows rich dynamical characteristics. Then, based on the pseudo-random numbers (PRNs) generated by the proposed system, a new construction method of multiple hash index chain is designed. And a new image encryption algorithm is designed according to the multiple hash index chain. The safety test results show that the design encryption algorithm has higher security performance. Finally, the 4-neurons-based HNN fractional-order system is implemented by Multisim circuit simulation. The experimental results show the feasibility of the theoretical analysis.

Design and implementation of a new fractional-order Hopfield neural network system

In this work, a novel chaotic system of fractional-order based on the model of Hopfield Neural Network (HNN) is proposed. The numerical solutions of the 4-neurons-based HNN fractional-order chaotic system are obtained by using the Adomain decomposition method. The dynamical performances of the 4-neurons-based HNN fractional-order chaotic system are explored through attractor trajectories, bifurcation diagrams, Lyapunov exponents, SE complexity and chaotic diagram based on SE complexity. In addition, the 4-neurons-based HNN fractional-order chaotic system is implemented based on the Multisim platform. The experimental results indicate that the 4-neurons-based HNN fractional-order chaotic system has rich dynamic behavior, and the influence of different order on the dynamical properties of the system are particularly great. This research will provide theoretical foundation and experimental basis for the hardware implementation and application of the 4-neurons-based HNN fractional-order chaotic system.