Single cell finite difference approximations ofO(kh2 +h4) for ?u/?x for one space dimensional nonlinear parabolic equation

Abstract

We report a new two-level explicit finite difference method of O(kh2 + h4) using three spatial grid points for the numerical solution of for the solution of one-space dimensional nonlinear parabolic partial differential equation subject to appropriate initial and Dirichlet boundary conditions. The method is shown to be unconditionally stable when applied to a linear equation. The proposed method is applicable to the problems both in cartesian and polar coordinates. Numerical examples are provided to demonstrate the efficiency and accuracy of the method discussed. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 408–415, 2000