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Solving Different Types of Differential Equations Using Modified and New Modified Adomian Decomposition Methods
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作者 Justina Mulenga Patrick Azere Phiri 《Journal of Applied Mathematics and Physics》 2023年第6期1656-1676,共21页
The Modified Adomian Decomposition Method (MADM) is presented. A number of problems are solved to show the efficiency of the method. Further, a new solution scheme for solving boundary value problems with Neumann cond... The Modified Adomian Decomposition Method (MADM) is presented. A number of problems are solved to show the efficiency of the method. Further, a new solution scheme for solving boundary value problems with Neumann conditions is proposed. The scheme is based on the modified Adomian decomposition method and the inverse linear operator theorem. Several differential equations with Neumann boundary conditions are solved to demonstrate the high accuracy and efficiency of the proposed scheme. 展开更多
关键词 Neumann Conditions modified adomian decomposition method Solution Scheme New modified adomian decomposition method Differential Equations
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Application of the Modified Adomian Decomposition Method on a Mathematical Model of COVID-19
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作者 Justina Mulenga Patrick Azere Phiri 《Journal of Applied Mathematics and Physics》 2023年第9期2597-2614,共18页
In this study, we constructed and analysed a mathematical model of COVID-19 in order to comprehend the transmission dynamics of the disease. The reproduction number (R<sub>C</sub>) was calculated via the n... In this study, we constructed and analysed a mathematical model of COVID-19 in order to comprehend the transmission dynamics of the disease. The reproduction number (R<sub>C</sub>) was calculated via the next generation matrix method. We also used the Lyaponuv method to show the global stability of both the disease free and endemic equilibrium points. The results showed that the disease-free equilibrium point is globally asymptotically stable if R<sub>C</sub> R<sub>C</sub> > 1. We further used the Adomian decomposition method and the modified Adomian decomposition method to obtain the solutions of the model. Numerical analysis of the model was done using Sagemath 9.0 software. 展开更多
关键词 COVID-19 Stability Analysis Equilibrium Points adomian decomposition method modified adomian decomposition method Numerical Analysis
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Solitary Wave Solutions of Discrete Complex Ginzburg-Landau Equation by Modified Adomian Decomposition Method 被引量:1
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作者 WANG Yue-Yue DAI Chao-Qing ZHANG Jie-Fang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第1期81-89,共9页
In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg-Landau equation with initial condition by considering the modified Adomian decomposition method (mADM), which is an efficient... In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg-Landau equation with initial condition by considering the modified Adomian decomposition method (mADM), which is an efficient method and does not need linearization, weak nonlinearity assumptions or perturbation theory. The numerical solutions are also compared with their corresponding analytical solutions. It is shown that a very good approximation is achieved with the analytical solutions. Finally, the modulational instability is investigated and the corresponding condition is given. 展开更多
关键词 discrete complex Ginzburg-Landau equation modified adomian decomposition method solitary wave solutions modulational instability
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Numerical Treatment of Initial Value Problems of Nonlinear Ordinary Differential Equations by Duan-Rach-Wazwaz Modified Adomian Decomposition Method 被引量:1
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作者 Omür Umut Serpil Yasar 《International Journal of Modern Nonlinear Theory and Application》 2019年第1期17-39,共23页
We employ the Duan-Rach-Wazwaz modified Adomian decomposition method for solving initial value problems for the systems of nonlinear ordinary differential equations numerically. In order to confirm practicality, robus... We employ the Duan-Rach-Wazwaz modified Adomian decomposition method for solving initial value problems for the systems of nonlinear ordinary differential equations numerically. In order to confirm practicality, robustness and reliability of the method, we compare the results from the modified Adomian decomposition method with those from the MATHEMATICA solutions and also from the fourth-order Runge Kutta method solutions in some cases. Furthermore, we apply Padé approximants technique to improve the solutions of the modified decomposition method whenever the exact solutions exist. 展开更多
关键词 adomian decomposition method Duan-Rach-Wazwaz modified adomian decomposition method Initial Value Problem Nonlinear Ordinary Differential Equation Mathematica Solution 4-th Order Runge Kutta method Pade Approximants
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The Approximate Analytical Solution of Non-Linear Equation for Simultaneous Internal Mass and Heat Diffusion Effects
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作者 Mayathevar Renugadevi Saminathan Sevukaperumal Lakshmanan Rajendran 《Natural Science》 2016年第6期284-294,共11页
For the first time a mathematical modelling of porous catalyst particles subject to both internal mass concentration gradients as well as temperature gradients, in endothermic or exothermic reactions has been reported... For the first time a mathematical modelling of porous catalyst particles subject to both internal mass concentration gradients as well as temperature gradients, in endothermic or exothermic reactions has been reported. This model contains a non-linear mass balance equation which is related to rate expression. This paper presents an approximate analytical method (Modified Adomian decomposition method) to solve the non-linear differential equations for chemical kinetics with diffusion effects. A simple and closed form of expressions pertaining to substrate concentration and utilization factor is presented for all value of diffusion parameters. These analytical results are compared with numerical results and found to be in good agreement. 展开更多
关键词 Chemical and Biological Systems modified adomian decomposition method Nonlinear Reaction Diffusion Porous Catalyst Particles Mass and Diffusion Effect
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Analytic Static Deflection Solutions of Uniform Cantilever Beams Resting on Nonlinear Elastic Rotational Boundary
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作者 Li-Kuo Chou Zhongjie Ye 《Journal of Mechanics Engineering and Automation》 2021年第4期105-113,共9页
In the paper,the analytic static deflection solutions of uniform cantilever beams resting on nonlinear elastic rotational boundary are developed by the Modified Adomian Decomposition Method(MADM).If the applied force ... In the paper,the analytic static deflection solutions of uniform cantilever beams resting on nonlinear elastic rotational boundary are developed by the Modified Adomian Decomposition Method(MADM).If the applied force function is an analytic function,then the deflection function can be derived and expressed in Maclaurin series.A recurrence relation for the coefficients of the Maclaurin series is derived.It is shown that the proposed solution method is accurate and efficient.The solution method can be successfully applied to the uniform cantilever beam and non-linear elastic rotational boundary problem. 展开更多
关键词 Deflection of uniform cantilever beam modified adomian decomposition method nonlinearity elastic rotational boundary
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Oxygen diffusion in a spherical cell subject to nonlinear Michaelis-Menten kinetics: Mathematical analysis by two exact methods
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作者 Hooman Fatoorehchi Hossein Abolghasemi +1 位作者 Laura Villafuerte Reza Zarghami 《International Journal of Biomathematics》 2017年第2期171-186,共16页
A nonlinear model representing oxygen diffusion accompanied by the Michaelis-Menten consumption kinetics inside a spherical cell is solved analytically by the differential transform method (DTM) and the modified Ado... A nonlinear model representing oxygen diffusion accompanied by the Michaelis-Menten consumption kinetics inside a spherical cell is solved analytically by the differential transform method (DTM) and the modified Adomian decomposition method (MADM). A perfect agreement between the literature data and the results from the proposed 展开更多
关键词 Cellular oxygen transfer mathematical modeling differential transformmethod modified adomian decomposition method.
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