Adomian decomposition method for time fractional diffusion-reaction equation

Document Type : Research and Reference

Authors

1 Mathematics Department, Faculty of Science, Aswan University, Aswan 81528, Egypt

2 Mathematics Department, Faculty of Science, Helwan University, Cairo, Egypt

Abstract

In this paper, the Adomian decomposition method (ADM) and specially its symbolic capability on the usage for determination of a solution to partial differential equations is explored. The Adomian decomposition method is used to solve the time fractional diffusion-reaction equation. This method is applied for two models of the time fractional diffusion-reaction equations (Autocatalytic reaction and Bistable and Schlogl models). The results given by this method show that, the effectiveness of the solution is closed Adomian decomposition method for time fractional diffusion-reaction equation to practical proposals of our research and is close to the exact solution. Moreover, the current method is introduced for the solution of the time fractional diffusion-reaction equation. The concentration of the species function is proportional directly with all the physical parameters in the “Bistable or Schlogl model” and inversely in case of” Autocatalytic model” respectively. The approximate solution considered that, the first and second driven terms of the decomposition are enough for the approximate solution.

Keywords

Main Subjects

Files

Share

How to cite

Statistics