Fourth‐order finite difference method for 2D parabolic partial differential equations with nonlinear first‐derivative terms

Abstract

We attempt to obtain a two‐level implicit finite difference scheme using nine spatial grid points of O(k2 + kh2 + h4) for solving the 2D nonlinear parabolic partial differential equation v1uxx + v2uyy = f(x, y, t, u, ux, uy, u1) where v1 and v2 are positive constants, with Dirichlet boundary conditions. The method, when applied to a linear diffusion‐convection problem, is shown to be unconditionally stable. Computational efficiency and the results of numerical experiments are discussed. Copyright © 1992 Wiley Periodicals, Inc.