A numerical method based on the Chebyshev cardinal functions for variable‐order fractional version of the fourth‐order 2D Kuramoto‐Sivashinsky equation

Abstract

In this article, the variable‐order (VO) time fractional 2D Kuramoto‐Sivashinsky equation is introduced, and a semidiscrete approach is presented through 2D Chebyshev cardinal functions (CCFs) for solving this equation. In the proposed method, we obtain a recurrent algorithm by using the finite difference method to approximate the VO fractional differentiation, the weighted finite difference method with parameter θ, and the approximation of the unknown function by the 2D CCFs. The differentiation operational matrices and the collocation technique are used to extract a linear system of algebraic equations which can be easily solved. The credibility of the developed method is examined on three numerical examples.