Higher-Order Numerical Techniques for Solving the Nonlinear Fisher Equation are Based on the Runge-Kutta Method - Kumari, Richa; Amrita,; Vimal, Vikash (Communications in Mathematics and Applications, 2025)
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 explores the utilization 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∞ errors with the exact solution, leading to high accuracy.
Keywords: Fisher’s problems; Method of lines; Finite difference methods; Strong stability preserving Runge-Kutta methods