Solving linear and non-linear space-time fractional reaction-diffusion equations by the Adomian decomposition method

2007 ◽  
Vol 74 (1) ◽  
pp. 138-158 ◽  
Author(s):  
Q. Yu ◽  
F. Liu ◽  
V. Anh ◽  
I. Turner
Keyword(s):  
Linear Space ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Reaction Diffusion ◽  
Space Time ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Adomian Decomposition ◽  
Non Linear ◽  
Fractional Reaction

Analytical Solution of Linear and Non-Linear Space-Time Fractional Reaction-Diffusion Equations

2010 ◽  
Vol 8 (1) ◽  
Author(s):  
Ahmet Yildirim ◽  
Sefa A Sezer
Keyword(s):  
Analytical Solution ◽  
Linear Space ◽  
Homotopy Perturbation Method ◽  
Reaction Diffusion ◽  
Space Time ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Homotopy Perturbation ◽  
Non Linear ◽  
Fractional Reaction

In this study, we present the homotopy perturbation method (HPM) for finding the analytical solution of linear and non-linear space-time fractional reaction-diffusion equations (STFRDE) on a finite domain. These equations are obtained from standard reaction-diffusion equations by replacing a second-order space deri-vative by a fractional derivative of order and a first-order time derivative by a fractional derivative of order. Some examples are given. Numerical results show that the homotopy perturbation method is easy to implement and accurate when applied to linear and non-linear space-time fractional reaction-diffusion equations.

scholarly journals Solving Some Linear and Nonlinear PDEs Using Laplace Adomian Decomposition Method

2018 ◽  
Vol 1 (2) ◽  
pp. 9-31
Author(s):  
Attaullah
Keyword(s):  
Decomposition Method ◽  
Evolution Equations ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Reaction Diffusion ◽  
Nonlinear Evolution Equations ◽  
Reaction Diffusion Equations ◽  
Nonlinear Pdes ◽  
Adomian Decomposition ◽  
Linear And Nonlinear

In this paper, Laplace Adomian decomposition method (LADM) is applied to solve linear and nonlinear partial differential equations (PDEs). With the help of proposed method, we handle the approximated analytical solutions to some interesting classes of PDEs including nonlinear evolution equations, Cauchy reaction-diffusion equations and the Klien-Gordon equations.

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