scholarly journals The Derivation of Convergence Analysis for the Multistage Adomian Decomposition Method for solving the Autonomous Van der Pol system

1999 ◽  
Vol 24 (3) ◽  
pp. 133-148
Author(s):  
Abbas AL-Bayati ◽  
Ann Al-Sawoor ◽  
Merna Samarji
Keyword(s):  
Convergence Analysis ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Van Der Pol ◽  
Adomian Decomposition

scholarly journals On a nonlinear singular one-dimensional parabolic equation and double Laplace decomposition method

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668653 ◽  
Author(s):  
Hassan Eltayeb Gadain ◽  
Imed Bachar
Keyword(s):  
Parabolic Equation ◽  
Laplace Transform ◽  
Convergence Analysis ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
One Dimensional ◽  
Double Laplace Transform ◽  
Adomian Decomposition ◽  
Laplace Decomposition Method

In this article, the double Laplace transform and Adomian decomposition method are used to solve the nonlinear singular one-dimensional parabolic equation. In addition, we studied the convergence analysis of our problem. Using two examples, our proposed method is illustrated and the obtained results are confirmed.

scholarly journals On Convergence Analysis and Analytical Solutions of the Conformable Fractional Fitzhugh–Nagumo Model Using the Conformable Sumudu Decomposition Method

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 243
Author(s):  
Suliman Alfaqeih ◽  
Emine Mısırlı
Keyword(s):  
Convergence Analysis ◽  
Decomposition Method ◽  
Fixed Point Theory ◽  
Adomian Decomposition Method ◽  
Nerve Impulse ◽  
Point Theory ◽  
Easy Method ◽  
Adomian Decomposition ◽  
Sumudu Transform ◽  
Mathematica Software

The current article studied a nonlinear transmission of the nerve impulse model, the Fitzhugh–Nagumo (FN) model, in the conformable fractional form with an efficient analytical approach based on a combination of conformable Sumudu transform and the Adomian decomposition method. Convergence analysis and error analysis were also carried out based on the Banach fixed point theory. We also provided some examples to support our results. The results obtained revealed that the presented approach is very fantastic, effective, reliable, and is an easy method to handle specific problems in various fields of applied sciences and engineering. The Mathematica software carried out all the computations and graphics in this paper.

scholarly journals Solutions of Volterra integral and integro-differential equations using modified Laplace Adomian decomposition method

2019 ◽  
Vol 15 (1) ◽  
pp. 5-18
Author(s):  
D. Rani ◽  
V. Mishra
Keyword(s):  
Differential Equations ◽  
Orthogonal Polynomials ◽  
Convergence Analysis ◽  
Decomposition Method ◽  
Bernstein Polynomials ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Modified Technique ◽  
Adomian Decomposition

Abstract In this paper, an effectual and new modification in Laplace Adomian decomposition method based on Bernstein polynomials is proposed to find the solution of nonlinear Volterra integral and integro-differential equations. The performance and capability of the proposed idea is endorsed by comparing the exact and approximate solutions for three different examples on Volterra integral, integro-differential equations of the first and second kinds. The results shown through tables and figures demonstrate the accuracy of our method. It is concluded here that the non orthogonal polynomials can also be used for Laplace Adomian decomposition method. In addition, convergence analysis of the modified technique is also presented.

scholarly journals Comparison of the Solution of the Van der Pol Equation Using the Modified Adomian Decomposition Method and Truncated Taylor Series Method

2020 ◽  
pp. 105-113
Author(s):  
Joel Ndam ◽  
O. Adedire
Keyword(s):  
Taylor Series ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Analytic Method ◽  
Series Method ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Taylor Series Method

In this paper, we compare the solution of the van der Pol equation obtained by using the truncated Taylor series method and the modified Adomian decomposition method with the solution obtained by the Poincare-Lindstedt (P-L) method. The approximating 4-component modified Adomian decomposition method behaves more like an approximate P-L analytic method than the tenth-order Taylor series. Also, with the addition of just one term, the approximating 5-component modified Adomian decomposition method produces a more convergent solution to that of P-L analytic method than the twenty second-order Taylor series approximation as the independent variable t representing time progressively increases. A general comparison of the two solutions revealed that the absolute errors generated by the approximating polynomial from the Taylor series are greater than the ones generated from the modified Adomian decomposition method. It was further revealed that very few components of the modified Adomian decomposition could yield a series of about 3 times the order of the one obtained by using the Taylor series method. Hence, we recommend the inclusion of the modified Adomian Decomposition Method in modern mathematical tools.

Numerical Solution of Nonlinear Volterra Integro-Differential Equations of Fractional Order by Using Adomian Decomposition Method

2014 ◽  
Vol 635-637 ◽  
pp. 1582-1585
Author(s):  
Li Feng Wang ◽  
Yun Peng Ma ◽  
Yong Qiang Yang
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Convergence Analysis ◽  
Fractional Order ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Computational Method ◽  
Numerical Example ◽  
Adomian Decomposition

In this work we present a computational method for for solving a class of nonlinear Volterra integro-differential equations of fractional order which is based on Adomian Decom-position Method. Convergence analysis is dependable enough to estimate the maximum absolute truncated error of the Adomian series solution. Numerical example is included to demonstrate the validity and applicability of the method.

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