Linear barycentric rational interpolation method for solving Kuramoto-Sivashinsky equation

Abstract

The Kuramoto-Sivashinsky (KS) equation being solved by the linear barycentric rational interpolation method (LBRIM) is presented. Three kinds of linearization schemes, direct linearization, partial linearization and Newton linearization, are presented to get the linear equation of the Kuramoto-Sivashinsky equation. Matrix equations of the discrete Kuramoto-Sivashinsky equation are also given. The convergence rate of LBRIM for solving the KS equation is also proved. At last, two examples are given to prove the theoretical analysis.

Keywords

• barycentric rational interpolation
• collocation method
• kuramoto-sivashinsky equation
• non-linear pde