A new 2-level implicit high accuracy compact exponential approximation for the numerical solution of nonlinear fourth order Kuramoto–Sivashinsky and Fisher–Kolmogorov equations

This paper discusses about a new compact 2-level implicit numerical method in the form of exponential approximation for finding the approximate solution of nonlinear fourth order Kuramoto–Sivashinsky and Fisher–Kolmogorov equations, which have applications in chemical engineering. The described method has an accuracy of temporal order two and a spatial order three (or four) on a variable (or constant) mesh. The approach has been demonstrated to be applicable to both non-singular and singular issues. This article has established the stability of the current technique. The suggested approach is used to solve several benchmark nonlinear parabolic problems associated in chemistry and chemical engineering, and the computed results are compared with the existing results to demonstrate the proposed method's superiority.