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

Year 2020, Volume: 10 Issue: 2, 415 - 427, 01.03.2020

R. K. Mohanty S. Sharma

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.

Keywords

Quasi-linear parabolic equations, Uniform mesh, Cubic Spline approximations, Burgers-Huxley equations

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