FOURTH-ORDER ACCURATE METHOD BASED ON HALF-STEP CUBIC SPLINE APPROXIMATIONS FOR THE 1D TIME-DEPENDENT QUASILINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS
FOURTH-ORDER ACCURATE METHOD BASED ON HALF-STEP CUBIC SPLINE APPROXIMATIONS FOR THE 1D TIME-DEPENDENT QUASILINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS
R. K. Mohanty, S. Sharma
[PDF]
Abstract
In this article, we discuss a fourth-order accurate scheme based on cubic spline approximations for the solution of quasilinear parabolic partial di erential equations (PDE). The stability of the scheme is discussed using a model linear PDE. Theproposed 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;