A SEMI-ANALYTIC APPROACH FOR SOLVING FISHER’S REACTION-DIFFUSION EQUATION BY METHOD OF LINES USING REPRODUCING KERNEL HILBERT SPACE METHOD
By
Gautam Patel and Kaushal Patel
Department of Mathematics, Veer Narmad South Gujarat University,
Surat-395007, Gujarat, India
Email: gautamvpatel26@gmail.com; kbpatel@vnsgu.ac.in
(Received: May 13, 2022; In format: August 24, 2022; Revised: November 19, 2022; Accepted: November 22, 2022)
DOI: https://doi.org/10.58250/jnanabha.2022.52229
Abstract
Many nonlinear systems are described with the nonlinear Fisher’s reaction-diffusion equation. The purpose of this work is to propose the method of lines to find out the solution of the Fisher’s reaction-diffusion equation in one dimension with quadratic and cubic nonlinearity using reproducing kernel Hilbert space method. In this method, the partial derivatives of the space variable are discretized to get a system of ODEs in the time variable and then solve the system of ODEs using reproducing kernel Hilbert space method. Four test examples are given to demonstrate the technique’s efficacy and applicability. The results are compared with the exact and existing numerical solutions by calculating the error norms L2 and L∞ at various time levels. It has been discovered that the recommended approach is not only simple to use, but also produces superior outcomes.
2020 Mathematical Sciences Classification: 35G31, 46E22, 65M20.
Keywords and Phrases: Method of Lines, Reproducing kernel Hilbert space method, Fisher’s reaction-diffusion equation.