An analytic solution for the space–time fractional advection–dispersion equation using the optimal homotopy asymptotic method

2012 ◽  
Vol 183 (10) ◽  
pp. 2098-2106 ◽  
Author(s):  
Ram K. Pandey ◽  
Om P. Singh ◽  
Vipul K. Baranwal ◽  
Manoj P. Tripathi
Keyword(s):  
Dispersion Equation ◽  
Asymptotic Method ◽  
Analytic Solution ◽  
Space Time ◽  
Advection Dispersion ◽  
Optimal Homotopy Asymptotic Method

scholarly journals Improved reproducing kernel method to solve space-time fractional advection-dispersion equation

2021 ◽  
Author(s):  
Tofigh Allahviranloo ◽  
Hussein Sahihi ◽  
Soheil Salahshour ◽  
D. Baleanu
Keyword(s):  
Dispersion Equation ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
Space Time ◽  
Finite Domain ◽  
Reproducing Kernel Method ◽  
Advection Dispersion ◽  
Schmidt Orthogonalization

In this paper, we consider the Space-Time Fractional Advection-Dispersion equation on a finite domain with variable coefficients. Fractional Advection- Dispersion equation as a model for transporting heterogeneous subsurface media as one approach to the modeling of the generally non-Fickian behavior of transport. We use a semi-analytical method as Reproducing kernel Method to solve the Space-Time Fractional Advection-Dispersion equation so that we can get better approximate solutions than the methods with which this problem has been solved. The main obstacle to solve this problem is the existence of a Gram-Schmidt orthogonalization process in the general form of the reproducing kernel method, which is very time-consuming. So, we introduce the Improved Reproducing Kernel Method, which is a different implementation for the general form of the reproducing kernel method. In this method, the Gram-Schmidt orthogonalization process is eliminated to significantly reduce the CPU-time. Also, the present method increases the accuracy of approximate solutions.

scholarly journals Optimal Homotopy Asymptotic Method for Solving Delay Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
N. Ratib Anakira ◽  
A. K. Alomari ◽  
I. Hashim
Keyword(s):  
Differential Equations ◽  
Asymptotic Method ◽  
Delay Differential Equations ◽  
Perturbation Methods ◽  
Analytic Solution ◽  
Approximate Analytic Solution ◽  
Initial Value ◽  
Optimal Homotopy Asymptotic Method ◽  
Delay Differential ◽  
First Time

We extend for the first time the applicability of the optimal homotopy asymptotic method (OHAM) to find the algorithm of approximate analytic solution of delay differential equations (DDEs). The analytical solutions for various examples of linear and nonlinear and system of initial value problems of DDEs are obtained successfully by this method. However, this approach does not depend on small or large parameters in comparison to other perturbation methods. This method provides us with a convenient way to control the convergence of approximation series. The results which are obtained revealed that the proposed method is explicit, effective, and easy to use.

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