A new hybrid technique based on nonpolynomial splines and finite differences for solving the Kuramoto–Sivashinsky equation

Abstract

The generalized Kuramoto–Sivashinsky equation arises frequently in engineering, physics, biology, chemistry, and applied mathematics, and because of its extensive applications, this important model has received much attention regarding obtaining numerical solutions. This article introduces a new hybrid technique based on nonpolynomial splines and finite differences for solving the Kuramoto–Sivashinsky equation approximately. Specifically, the truncation error is studied to examine the convergence order of the proposed scheme, some problems are given to show its viability and effectiveness, and the norm errors are determined to compare the current method with the analytic solution and some other methods from the literature.

An efficient scheme for solving nonlinear generalized kuramoto-sivashinksy processes

“…Many authors have numerically investigated the KS equation, as referenced in [25][26][27][28][29][30][31][32][33], while the space discretization has been systematically conducted using spectral methods. A variety of methods have been applied for the discretization of time, such as Runge-Kutta methods with different orders, a split scheme of variable time, in accordance with the Strang-split method [32,33], and implicit-explicit techniques [34][35][36].…”