Efficient algorithm to study the class of Burger's Fisher equation. (30th August 2022)

• Record Type: Journal Article
• Authors: Patel, Yogeshwari F.; Dhodiya, Jayesh M.
• Is Part Of: International journal of applied nonlinear science. Volume 3:Number 3(2022)
• Page Start: 242
• Page End: 266
• Publication Date: 2022-08-30
• Subjects: Fisher reaction diffusion equation -- reduced differential transform method -- RDTM -- analytical solution -- error analysis -- convergence method; Science -- Mathematical models -- Periodicals; Engineering -- Mathematical models -- Periodicals; Nonlinear theories -- Periodicals; 501.5118
• Languages: English
• ISSNs: 1752-2862

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.