Convergence Analysis and Implementation of Adomian Decomposition Method on Second-order Oscillatory Problems

2017 ◽  
Vol 2 (5) ◽  
pp. 1-12 ◽  
Author(s):  
J Sunday
Keyword(s):  
Convergence Analysis ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Second Order ◽  
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.

Solutions of Second Order Three Point BVP Using Combination of Adomian Decomposition Method and Reproducing Kernel Method

2015 ◽  
Vol 4 (1) ◽  
pp. 73-76
Author(s):  
Hamood ur Rehman ◽  
Muhammad Usman Malik ◽  
Muzammal Iftikhar ◽  
Muhammad Younis ◽  
M. Shoaib Saleem
Keyword(s):  
Decomposition Method ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Adomian Decomposition Method ◽  
Second Order ◽  
Reproducing Kernel Method ◽  
Adomian Decomposition
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