FOURTH-ORDER ACCURATE METHOD BASED ON HALF-STEP CUBIC SPLINE APPROXIMATIONS FOR THE 1D TIME-DEPENDENT QUASILINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS

Özet

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.