Higher-order numerical technique based on strong stability preserving method for solving nonlinear Fisher equation

Authors

  • VIKASH VIMAL NATIONAL INSTITUTE OF TECHNOLOGY PATNA

Keywords:

Fisher’s problems, Method of lines, Finite difference methods, Strong stability preserving Runge-Kutta methods.

Abstract

This paper presents higher-order numerical methods for solving nonlinear Fisher
equations. These types of equations arise in various fields of sciences and engineering,
the main application of this equation has been found in the biomedical sciences.
The solution of this equation helps to determine the size of the brain tumor. In
this paper, we have constructed the numerical method based on the method of lines
and higher order strong stability preserving schemes of order three and four. These
schemes are explicit in nature and easy to implement specially to solve the nonlinear
problems. Due to the stability-preserving nature of the scheme, the restriction on
time steps is very mild. These schemes are very practical to use and produce very
accurate results. Various test problems are considered to validate the scheme along
with a comparison of L2 and L∞ errors with the exact solution, resulting in high
accuracy. The scheme is found to be better compared to existing schemes with less
computational effort

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Published

20-02-2025

How to Cite

VIMAL, V. (2025). Higher-order numerical technique based on strong stability preserving method for solving nonlinear Fisher equation. Communications in Mathematics and Applications, 15(3). Retrieved from https://rgnpublications.com/journals/index.php/cma/article/view/2806

Issue

Vol. 15 No. 3 (2024)

Section

Research Article

License

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