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Modified asymptotic adomian decomposition method for solving Boussinesq equation of groundwater flow

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Applied Mathematics and Mechanics(English Edition) 2014年第4期35卷 481-488页

作者：陈芳刘青泉 Key Laboratory for Mechanics in Fluid Solid Coupling Systems Institute of Mechanics Chinese Academy of Sciences School of Applied Science Beijing Information Science and Technology University

The adomian decomposition method （ADM） is an approximate analytic method for solving nonlinear equations. Generally, an approximate solution can be ob- tained by using only a few terms. However, in applications, we need to use it flexibly according to the real problem. In this paper, based on the ADM, we give a modified asymptotic adomian decomposition method and use it to solve the nonlinear Boussinesq equation describing groundwater flows. The example shows effectiveness of the modified asymptotic adomian decomposition method.

关键词： groundwater flow Boussinesq equation adomian decomposition asymp-totic adomian decomposition

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

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

On the solutions of an oxygen absorption model

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International Journal of Biomathematics 2014年第6期7卷 21-26页

作者： Lazhar Bougoffa Department of Mathematics Faculty of ScienceAl Imam Mohammad Ibn Saud Islamic University (IMSIU) P. O. Box 90950 Riyadh 11623 Saudi Arabia

In this note we present the adomian decomposition method for solving a simple model for the diffusion and absorption of oxygen in tissue. The method is examined for computational efficiency and accuracy.

关键词： Oxygen absorption model adomian decomposition asymptotic decomposi-tion method a priori estimate.

广义Black-Scholes方程的adomian级数解及其数值计算

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高等学校计算数学学报 2016年第1期38卷 1-17页

作者：傅强朱哲殷涛重庆大学经济与工商管理学院重庆大学数学与统计学院

In this paper we present a numerical method for a generalized BlackScholes partial differential equation for option *** first derive its series solution whose coefficients are determined by recursion formulas involving integrals by means of the adomian *** we present a numerical scheme based on the trapezoidal rule instead of direct integral method for the Adomain series *** results show the effectiveness of the present method.

关键词： Option pricing Black-Scholes equation adomian decomposition Trapezoidal rule

Numerical Solutions of Three-Dimensional Coupled Burgers’ Equations by Using Some Numerical Methods

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Journal of Applied Mathematics and Physics 2016年第11期4卷 2011-2030页

作者： Fatheah Ahmad Alhendi Aisha Abdullah Alderremy Department of Mathematics King Abdulaziz University Jeddah Kingdom of Saudi Arabia Department of Mathematics King Khaild University Abha Kingdom of Saudi Arabia

In this paper, we found the numerical solution of three-dimensional coupled Burgers’ Equations by using more efficient methods: Laplace adomian decomposition method, Laplace transform homotopy perturbation method, variational iteration method, variational iteration decomposition method and variational iteration homotopy perturbation method. Example is examined to validate the efficiency and accuracy of these methods and they reduce the size of computation without the restrictive assumption to handle nonlinear terms and it gives the solutions rapidly.

关键词： Three-Dimensional Coupled Burgers’ Equations Laplace Transform adomian decomposition Homotopy Perturbation Variational Iteration Method