Fourth‐order compact schemes of a heat conduction problem with Neumann boundary conditions

Abstract

AbstractIn this article, a set of fourth‐order compact finite difference schemes is developed to solve a heat conduction problem with Neumann boundary conditions. It is derived through the compact difference schemes at all interior points, and the combined compact difference schemes at the boundary points. This set of schemes is proved to be globally solvable and unconditionally stable. Numerical examples are provided to verify the accuracy.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007