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Homotopy Perturbation Method for the Generalized Hirota-Satsuma Coupled KdV Equation

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Applied Mathematics 2012年第12期3卷 1983-1989页

作者： dalal A. maturi Department of Mathematics Faculty of Science King AbdulAziz University Jeddah Saudi Arabia

In this paper, we consider the homotopy perturbation method (HPM) to obtain the exact solution of Hirota-Satsuma Coupled KdV equation. The results reveal that the proposed method is very effective and simple and can b... 详细信息

关键词： Homotopy Perturbation Method Generalized Hirota-Satsuma Coupled KdV Equation

Adomian Decomposition Method for Solving Fractional Time-Klein-Gordon Equations Using Maple

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Applied Mathematics 2023年第6期14卷 411-418页

作者： dalal Albogami dalal maturi Hashim Alshehri Department of Mathematics King Abdulaziz University Jeddah Saudi Arabia

Adomian decomposition is a semi-analytical approach to solving ordinary and partial differential equations. This study aims to apply the Adomian Decomposition Technique to obtain analytic solutions for linear and nonlinear time-fractional Klein-Gordon equations. The fractional derivatives are computed according to Caputo. Examples are provided. The findings show the explicitness, efficacy, and correctness of the used approach. Approximate solutions acquired by the decomposition method have been numerically assessed, given in the form of graphs and tables, and then these answers are compared with the actual solutions. The Adomian decomposition approach, which was used in this study, is a widely used and convergent method for the solutions of linear and non-linear time fractional Klein-Gordon equation.

关键词： Adomian Decomposition Klein-Gordon Fractional Calculus

Variational Iteration Method for Solving Boussinesq Equations Using Maple

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Applied Mathematics 2022年第12期13卷 960-967页

作者： Ameera Aljuhani dalal maturi Hashim Alshehri Department of Mathematics King Abdul Aziz University Jeddah KSA

In this study, we applied the variational iteration method to solve the Boussinesq time equation. Bossiness’s article from 1872 introduced the equations that are now known as the Boussinesq equations. Numerical methods are commonly utilized to solve nonlinear equation systems. Several research papers have documented the values of the variational iteration method and its applications for various categories of differential equations. A comparison of the exact and numerical solutions was obtained using the variational iteration method. The variational iteration method shows that the proposed method is very effective and convenient. The results are shown for different specific cases of the problem. The variational iteration method is useful in numerical simulations and approximate analytical solutions, and it is used to resolve nonlinear differential equations in various situations using Maple. For example, the linear Boussinesq equation was resolved using the variational iteration method. By comparing the numerical results, we found that the variable repetition method produced accurate results and was close to the exact solution, allowing it to be widely applied to the Boussinesq equation. This proves the effectiveness of the method and the capability to quickly and effectively obtain the numerical number solution related to the exact solution using the Maple 18 program. Additionally, the outcomes are extremely precise.

关键词： Boussinesq Equations Maple 18 Variational Iteration Method

Variational Iteration Method for Solving Time Fractional Burgers Equation Using Maple

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Applied Mathematics 2023年第5期14卷 336-348页

作者： Fayza Alwehebi Aatef Hobiny dalal maturi Department of Mathematics King Abdulaziz University Jeddah Saudi Arabia

The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this technique. Tables and images were used to present the collected numerical results. The difference between the exact and numerical solutions demonstrates the effectiveness of the Mabel program’s solution, as well as the accuracy and closeness of the results this method produced. It also demonstrates the Mabel program’s ability to quickly and effectively produce the numerical solution.

关键词： Variational Iteration Method Time Fractional Burgers Equation Maple18

Adomian Decomposition Method for Solving Time Fractional Burgers Equation Using Maple

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Applied Mathematics 2023年第5期14卷 324-335页

作者： Fayza Alwehebi Aatef Hobiny dalal maturi Department of Mathematics King Abdulaziz University Jeddah Saudi Arabia

In this paper, the Adomian decomposition method was used to solve the Time Fractional Burger equation using Mabel program. This method was applied to a number of examples of the Time Fractional Burger Equation. The obtained numerical results were presented in the form of tables and graphics. The difference between the exact solutions and the numerical solutions shows us the effectiveness of the solution using the Mabel program and that this method gave accurate results and was close to the exact solution, in addition to its ability to obtain the numerical solution quickly and efficiently using the Mabel program.

关键词： Adomian Decomposition Method Time Fractional Burgers Equation Maple 18

The Adomian Decomposition Method for Solving Nonlinear Partial Differential Equation Using Maple

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Advances in Pure Mathematics 2021年第6期11卷 595-603页

作者： dalal Adnan maturi Honaida Mohammed Malaikah Department of Mathematics Faculty of Science King Abdulaziz University Jeddah Saudi Arabia

The nonlinear partial differential equation is solved using the Adomian decomposition method (ADM) in this article. A number of examples have been provided to illustrate the numerical results, which is the comparison of the exact and numerical solutions, and it has been discovered through the tables that the amount of error between the exact and numerical solutions is very small and almost non-existent, and the graph also shows how the exact solution of absolutely applies to the numerical solution. This demonstrates the precision of the Adomian decomposition method (ADM) for solving the nonlinear partial differential equation with Maple18. And that in terms of obtaining numerical results, this approach is characterized by ease, speed, and high accuracy.

关键词： Nonlinear Partial Differential Equation Adomian Decomposition Method Maple18

Adomian Decomposition Method for Solving Boussinesq Equations Using Maple

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Applied Mathematics 2023年第2期14卷 121-129页

作者： Ameera Aljuhani dalal maturi Hashim Alshehri Department of Mathematics King Abdulaziz University Jeddah Saudi Arabia

This paper uses the Adomian Decomposition Method (ADM) to solve Boussinesq equations using Maple. The Boussinesq approximation for water waves is a weakly nonlinear and long-wave approximation in fluid dynamics. The approximation is named after Joseph Boussinesq, who developed it in response to John Scott Russell’s observation of a wave of translation (also known as solitary wave or soliton). Bossinesq’s article from 1872 introduced the equations that are now known as the Boussinesq equations. Numerical methods are commonly utilized to solve nonlinear equation systems. In this paper, we investigate a nonlinear singly perturbed advection-diffusion problem. Using the usual Adomian Decomposition Method, we formulate an approximate linear advection-diffusion problem and investigate several practical numerical approaches for solving it (ADM). The Adomian Decomposition Method (ADM) is a powerful tool for numerical simulations and approximation analytic solutions. The Adomian Decomposition Method (ADM) is used to solve nonlinear advection differential equations using Maple by illustrating numerous examples. The findings are presented in the form of tables and graphs for several examples. For various examples, the findings are presented in the form of tables and graphs. The difference between the precise and numerical solutions indicates the Maple program solution’s efficacy, as well as the ease and speed with which it was acquired.

关键词： Adomian Decomposition Method Boussinesq Equations Maple 18

Higher Order Implicit Scheme for Nonlinear Time-Dependent Convection-Diffusion- Reaction Equation

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American Journal of Computational Mathematics 2022年第2期12卷 232-248页

作者： Uzair Ahmed Daoud Suleiman Mashat dalal Adnan maturi Department of Mathematics King Abdulaziz University Jeddah Saudi Arabia

A mathematical model comprising of nonlinear reaction, diffusion, and convection mechanisms seen in natural and anthropogenic processes is numerically investigated here. It is proposed that a higher order numerical scheme of finite difference method be used in conjunction with an iterative approach in order to solve the nonlinear one dimensional convection-diffusion-reaction equation. To account for the wide variety of physical characteristics and boundary conditions, an iterative approach is presented that yields a reliable and precise solution every time. We examined the accuracy and operational efficiency of two distinct finite difference approaches. The efficiency of the system is determined by comparing the estimated results to the appropriate analytical solution by adhering to established norms. Coherence and convergence were analyzed for each approach. The simulation results demonstrate the efficacy and accuracy of these methods in solving nonlinear convection- diffusion-reaction equations. Convection-diffusion-reaction equation modeling is critical for employing the offered results in heat and mass transport processes.

关键词： Finite Difference Method (FDM) Crank-Nicholson (CN) Fourth Order Implicit (FOI) Convection-Diffusion-Reaction (CDR)

Finite Difference Approximation for Solving Transient Heat Conduction Equation of Copper

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Advances in Pure Mathematics 2020年第5期10卷 350-358页

作者： dalal Adnan maturi Nujud Makhdhur Alsulami Eman Salem Alaidarous Department of Mathematics Faculty of Science King Abdulaziz University Jeddah Saudi Arabia

In this paper, a numerical technique is proposed to obtain the solution for transient heat conduction equation of Copper. The copper element is characterized by many characteristics;the most important of which is its high ability to conduct heat and electrical conductivity, in addition to being a flexible and malleable metal that is easy to form without being broken, making it one of the basic minerals that humans have benefited from for thousands of years, it is one of the first minerals. That has been discovered and extracted, and still plays a major role in the development of societies. The obtained solutions are compared with the available exact solutions and the obtained solutions using the finite difference method. The results indicate that the finite difference method is a highly effective method for obtaining approximate solutions for the thermal conductivity equation for copper. It is also clear from the numerical results from copper in the high conductivity of heat and electricity.

关键词： Finite Difference Approximation Transient Heat Conduction Equation Copper Matlab