Higher-order numerical techniques for solving the nonlinear Fisher equation are based on the Runge-Kutta method

Authors

  • VIKASH VIMAL NATIONAL INSTITUTE OF TECHNOLOGY PATNA
  • RICHA KUMARI

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 ap-
plication 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 explores the utiliza-
tion of advanced numerical techniques, such as the method of lines and higher-order strong
stability preserving schemes of order four and stage seven, to approximate solutions to the
Fisher equation with higher-order accuracy. These schemes are explicitly designed and easy
to implement, especially for addressing nonlinear problems. Their stability-preserving nature
ensures only mild restrictions on time steps. This scheme is then tested on two examples and
the results show that it is more efficient methods and requires less computing time. Various
test problems are examined to verify the scheme’s performance, including a comparison of
L2 and L_{\infty} errors with the exact solution, leading to high accuracy.

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Published

20-08-2025

How to Cite

VIMAL, V., & KUMARI, R. (2025). Higher-order numerical techniques for solving the nonlinear Fisher equation are based on the Runge-Kutta method. Communications in Mathematics and Applications, 16(2). Retrieved from https://www.journals.rgnpublications.com/index.php/cma/article/view/2912

Issue

Vol. 16 No. 2 (2025)

Section

Research Article

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