Numerical Solution of the Goursat Problem

A.I.M. Ismail, M.A.S. Nasir, and A.Z. Talib (Malaysia)


Goursat problem, finite difference schemes, arithmeticmean, harmonic mean


The Goursat problem, associated with hyperbolic partial differential equations, arises in several areas of applications. Several finite difference schemes have been proposed to solve the Goursat problem. Amongst these schemes is a scheme which implements harmonic mean averaging of function values. A comparative study which has been carried out concluded that harmonic mean averaging yielded more accurate results than arithmetic mean averaging. However, there seemed to be discrepancies between the conclusions and the displayed results. In this paper, we present the results of a comparative study which we have conducted on three Goursat problems over a range of grid sizes. Our results indicate that arithmetic mean averaging is more accurate than harmonic mean averaging. We also show that arithmetic mean averaging has an advantage when applied to linear Goursat problems.

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