Fourth-order accurate method based on half-step cubic spline approximations for the 1d time-dependent quasilinear parabolic partial differential equations

Abstract

In this article, we discuss a fourth-order accurate scheme based on cubic spline approximations for the solution of quasilinear parabolic partial differential equations (PDE). The stability of the scheme is discussed using a model linear PDE. The proposed method is tested on Burgers’ equations in polar coordinates and Burgers-Huxley equation.