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The Appearance of Noise Terms in Modified Adomian Decomposition Method for Quadratic Integral Equations

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American Journal of Computational Mathematics 2012年第2期2卷 125-129页

作者： huda Omar bakodah Department of Mathematics Sciences Faculty for Girls King Abdulaziz University Jeddah Saudi Arabia

In this paper, we apply the modified Adomian Decomposition Method to get the numerical solutions of Quadratic integral equations. The appearance of noise terms in Decomposition Method was investigated. The method was ... 详细信息

关键词： Modified Adomian Decomposition method Quadratic integral equation The noise Terms

Modified Adomain Decomposition Method for the Generalized Fifth Order KdV Equations

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American Journal of Computational Mathematics 2013年第1期3卷 53-58页

作者： huda O. bakodah Department of Mathematics Science Faculty for Girls King Abdulaziz University Jeddah KSA

New modified Adomian decomposition method is proposed for the solution of the generalized fifth-order Korteweg-de Vries (GFKdV) equation. The numerical solutions are compared with the standard Adomian decomposition method and the exact solutions. The results are demonstrated which confirm the efficiency and applicability of the method.

关键词： Modified Adomian Decomposition Method Fifth Order KdV Equation Solitary-Wave Solution

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

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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

A New Modification of the Method of Lines for First Order Hyperbolic PDEs

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Applied Mathematics 2014年第10期5卷 1457-1462页

作者： Fatmah M. Alabdali huda Omar bakodah Department of Mathematics Science Faculty for Girls King Abdulaziz University Jeddah KSA

A new modification of the Method of Lines is proposed for the solution of first order partial differential equations. The accuracy of the method is shown with the matrix analysis. The method is applied to a number of ... 详细信息

关键词： Method of Lines First-Order Hyperbolic Equation Numerical Solution

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

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

Efficient Decomposition Shooting Method for Solving Third-Order Boundary Value Problems

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International Journal of Modern Nonlinear Theory and Application 2023年第3期12卷 81-98页

作者： Nawal Al-Zaid Kholoud Alzahrani huda bakodah Mariam Al-Mazmumy Department of Mathematics Faculty of Science University of Jeddah Jeddah Saudi Arabia

The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and, the modified shooting method. A complete derivation of the proposed method has been provided, in addition to its numerical implementation and, validation via the utilization of the Runge-Kutta method and, other existing methods. The method has been applied to diverse test problems and turned out to perform remarkably. Lastly, the simulated numerical results have been graphically illustrated and, also supported by some absolute error comparison tables.

关键词： Linear Third Order BVPs Shooting Method Adomian Decomposition Method Two-Point Boundary Value Problem

Numerical Solutions of the Regularized Long-Wave (RLW) Equation Using New Modification of Laplace-Decomposition Method

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Advances in Pure Mathematics 2013年第1期3卷 159-163页

作者： Nawal A. Al-Zaid huda O. bakodah Fathiah A. Hendi Department of Mathematics Science Faculty for Girls King Abdulaziz University Jeddah KSA

In this paper the new modification of Laplace Adomian decomposition method (ADM) to obtain numerical solution of the regularized long-wave (RLW) equation is presented. The performance of the method is illustrated by s... 详细信息

关键词： Adomian Decomposition Method Regularized Long-Wave (RLW) Laplace Transform

Soliton Solutions and Numerical Treatment of the Nonlinear Schrodinger’s Equation Using Modified Adomian Decomposition Method

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Journal of Applied Mathematics and Physics 2016年第12期4卷 2215-2232页

作者： Abeer Al-Shareef Alyaa A. Al Qarni Safa Al-Mohalbadi huda O. bakodah Department of Mathematics Faculty of Science King Abdulaziz University Jeddah Kingdom of Saudi Arabia Department of Mathematics Faculty of Science Blqarn Campus Bisha University Bisha Kingdom of Saudi Arabia Department of Mathematics Faculty of Science Al Faisaliah Campus King Abdulaziz University Jeddah Kingdom of Saudi Arabia

In this paper, the improved Adomian decomposition method (ADM) is applied to the nonlinear Schrödinger’s equation (NLSE), one of the most important partial differential equations in quantum mechanics that governs the propagation of solitons through optical fibers. The performance and the accuracy of our improved method are supported by investigating several numerical examples that include initial conditions. The obtained results are compared with the exact solutions. It is shown that the method does not need linearization, weak or perturbation theory to obtain the solutions.

关键词： Nonlinear Differential Equation Schrödinger Equation Adomian Decomposition Reliable Technique