A numerical algorithm based on the modified quintic B-splines for the Fisher’s equation

• Published in: AIP conference proceedings Vol. 3081; no. 1
• Main Authors: Anisha, Rohila, Rajni
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Melville American Institute of Physics 29.04.2024
• Subjects: Algorithms; B spline functions; Differential equations; Numerical analysis; Numerical methods; Quadratures; Reaction-diffusion equations; Runge-Kutta method; Wave propagation
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0196463

The numerical solutions of Fisher’s equation are obtained by using a differential quadrature method based on quintic B-spline functions. Fisher equation represents a class of reaction-diffusion equations that describe wave propagation and population development. In this method, the Fisher’s equation is discretized by using quintic B-spline functions to get a system of ordinary differential equations. The system of ordinary differential equations is solved by using SSPRK43 method, which is a varient of Runge Kutta method and is more stable than the parent method. The numerical results have been presented in tabular form and also depicted in graphs. The proposed method is applied on two numerical problems and is compared with the results obtained by other numerical method.