We combine fourth order boundary value methods (BVMs) for discretizing the temporal variable with fourth order compact difference scheme for discretizing the spatial variable to solve one dimensional heat equations. The resulting compact difference scheme achieves fourth order accuracy in both temporal and spatial variables, and is unconditionally stable due to the favorable stability property of BVMs. Numerical results are presented to demonstrate the accuracy and efficiency of the new compact difference scheme, compared to the standard second order Crank-Nicolson scheme.
Mathematics Subject Classification: 65N06, 65N55, 65F10.
Technical Report 333-02, Department of Computer Science, University of Kentucky, Lexington, KY, 2002.
This research was supported in part by the U.S. National Science Foundation under the grant CCR-9902022, CCR-9988165, and CCR-0092532, in part by the U.S. Department of Energy under grant DE-FG02-02ER45961, in part by the Japanese Research Organization for Information Science & Technology, and in part by the University of Kentucky Research Committee.