Title: Efficient algorithm to study the class of Burger's Fisher equation

Authors: Yogeshwari F. Patel; Jayesh M. Dhodiya

Addresses: Department of Mathematical Sciences, P.D. Patel Institute of Applied Sciences, Charotar University of Science and Technology, Changa, Anand, Gujarat-388421, India ' Applied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology, Surat, Gujarat-395007, India

Abstract: This paper aims to provide an effective analytical approach to study the family of Fisher's reaction-diffusion equation, namely the reduced differential transform method. These equations are well-known in mathematical biology and have a wide range of applications, including population dynamics, combustion theory, genetic propagation, stochastic processes, and a prototype model for a spreading flame. The proposed method's leverage over other analytical approaches is its capability to handle the nonlinear terms without discretisation, perturbation, or calculation of unneeded terms. The obtained results are more precise and reliable and show a high level of agreement with the exact solution. The convergence criteria and error analysis are also addressed in this paper. The straightforward applicability of the proposed method to convert the complex nonlinear partial differential equation into a simple algebraic system makes it a promising computational method. In this paper, we also provide the algorithm which can be easily implemented in MATLAB.

Keywords: Fisher reaction diffusion equation; reduced differential transform method; RDTM; analytical solution; error analysis; convergence method.

DOI: 10.1504/IJANS.2022.125308

International Journal of Applied Nonlinear Science, 2022 Vol.3 No.3, pp.242 - 266

Received: 02 Feb 2022
Accepted: 01 Jun 2022
Published online: 06 Sep 2022 *