On the Solution of Bratu’s Initial Value Problem in the Liouville-Caputo Sense by ARA Transform and Decomposition Method

2021 ◽  
Author(s):  
Suleyman Cetinkaya ◽  
Ali Demir
Keyword(s):  
Initial Value Problem ◽  
Decomposition Method ◽  
Initial Value

scholarly journals Modified Adomian Decomposition Method to Solve Generalized Emden–Fowler Systems for Singular IVP

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Aisha Abdullah Alderremy ◽  
Tarig M. Elzaki ◽  
Mourad Chamekh
Keyword(s):  
Initial Value Problem ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Initial Value ◽  
Generalized System ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Singular Initial Value Problem

An adeptness modified Adomian decomposition method (MADM) is proposed to solve a generalized system of Emden–Fowler type. By a few examples, it is shown that this method can overcome a singular initial value problem.

scholarly journals Numerical Simulation of the FitzHugh-Nagumo Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
A. A. Soliman
Keyword(s):  
Numerical Simulation ◽  
Initial Value Problem ◽  
Iteration Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Initial Value ◽  
Variational Iteration ◽  
Adomian Decomposition ◽  
Nagumo Equations

The variational iteration method and Adomian decomposition method are applied to solve the FitzHugh-Nagumo (FN) equations. The two algorithms are illustrated by studying an initial value problem. The obtained results show that only few terms are required to deduce approximated solutions which are found to be accurate and efficient.

Numerical solutions of the initial value problem for fractional differential equations by modification of the Adomian decomposition method

2014 ◽  
Vol 17 (2) ◽  
Author(s):  
Neda Khodabakhshi ◽  
S. Mansour Vaezpour ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Initial Value Problem ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
Adomian Decomposition Method ◽  
Initial Value ◽  
Adomian Decomposition ◽  
Fractional Differential

AbstractIn this paper, we extend a reliable modification of the Adomian decomposition method presented in [34] for solving initial value problem for fractional differential equations.In order to confirm the applicability and the advantages of our approach, we consider some illustrative examples.

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