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Numerical Treatment of Initial-Boundary Value Problems with Mixed Boundary Conditions

American Journal of Computational Mathematics 2018年第2期8卷 153-174页

作者： nawal Abdullah alzaid Huda Omar Bakodah Department of Mathematics King Abdulaziz University Jeddah KSA

In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary conditions for linear and nonlinear partial differential equations. The method is applied to different forms of heat and wave equations as illustrative examples to exhibit the effectiveness of the method. The method provides the solution in a rapidly convergent series with components that can be computed iteratively. The numerical results for the illustrative examples obtained show remarkable agreement with the exact solutions. We also provide some graphical representations for clear-cut comparisons between the solutions using Maple software.

关键词： Decomposition Method Modified Adomian Decomposition Method Linear and Nonlinear Partial Differential Equations Mixed Boundary Conditions Initial-Boundary Value Problem

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Approximate Solution Method of the Seventh Order KdV Equations by Decomposition Method

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Journal of Applied Mathematics and Physics 2019年第9期7卷 2148-2155页

作者： nawal Abdullah alzaid Bashayr Ali Alrayiqi Department of Mathematics Faculty of Science University of Jeddah Jeddah KSA Department of Mathematics College of Science and Arts King Abdulaziz University Rabigh KSA

In this paper, Adomian decomposition method (ADM) is implemented to approximate the solution of the Korteweg-de Vries (KdV) equations of seventh order, which are Kaup-Kuperschmidt equation and seventh order Kawahara equation. The results obtained by the ADM are compared with the exact solutions. It is found that the ADM is very efficient and convenient and can be applied to a large class of problems. The conservation properties of solution are examined by calculating the first three invariants.

关键词： Adomian Decomposition Method Kaup-Kuperschmidt Seventh-Order KdV Equation Seventh-Order Kawahara Equation Conservation Laws

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Adomian Modification Methods for the Solution of Chebyshev’s Differential Equations

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Applied Mathematics 2023年第8期14卷 512-530页

作者： Mariam Al Mazmumy Aishah Alsulami Huda Bakodah nawal alzaid Department of Mathematics College of Science University of Jeddah Jeddah Saudi Arabia

The current study examines the important class of Chebyshev’s differential equations via the application of the efficient Adomian Decomposition Method (ADM) and its modifications. We have proved the effectiveness of the employed methods by acquiring exact analytical solutions for the governing equations in most cases;while minimal noisy error terms have been observed in a particular method modification. Above all, the presented approaches have rightly affirmed the exactitude of the available literature. More to the point, the application of this methodology could be extended to examine various forms of high-order differential equations, as approximate exact solutions are rapidly attained with less computation stress.

关键词： ADM Modifications Methods Chebyshev’s Differential Equations IVPs Series Solutions

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On the Application of Adomian Decomposition Method to Special Equations in Physical Sciences

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American Journal of Computational Mathematics 2023年第3期13卷 387-397页

作者： Aishah Alsulami Mariam Al-Mazmumy Huda Bakodah nawal alzaid Department of Mathematics College of Science University of Jeddah Jeddah Saudi Arabia

The current manuscript makes use of the prominent iterative procedure, called the Adomian Decomposition Method (ADM), to tackle some important special differential equations. The equations of curiosity in this study are the singular equations that arise in many physical science applications. Thus, through the application of the ADM, a generalized recursive scheme was successfully derived and further utilized to obtain closed-form solutions for the models under consideration. The method is, indeed, fascinating as respective exact analytical solutions are accurately acquired with only a small number of iterations.

关键词： Iterative Scheme Adomian Decomposition Method Initial-Value Problems Singular Ordinary Differential Equations

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