An efficient computational approach for solving two-dimensional extended Fisher–Kolmogorov equation

Abstract

The extended Fisher–Kolmogorov (EFK) system is a strong nonlinear fourth-order reaction diffusion evolution equation. So far, the numerical methods for solving this problem are only a few. This paper deals with the finite difference solution to the two-dimensional EFK equation. The scheme is proved to be uniquely solvable and second-order convergent in both time and space in maximum norm. Finally, some numerical examples have been illustrated to verify the efficiency and simplicity of the proposed technique.

Keywords:

• Extended Fisher–Kolmogorov equation
• linearized difference scheme
• solvability
• convergence

MSC:

• 65M06
• 65M12
• 65M15

Acknowledgments

The authors are very grateful to reviewers for carefully reading this work and that their comments and suggestions have really improved the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).