A fourth-order compact finite difference scheme for the Goursat problem

Mohd Agos Salim Nasir, and Ahmad Izani Md Ismail, (2013) A fourth-order compact finite difference scheme for the Goursat problem. Sains Malaysiana, 42 (3). 341 -346. ISSN 0126-6039

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Abstract

A high-order uniform Cartesian grid compact finite difference scheme for the Goursat problem is developed. The basic idea of high-order compact schemes is to find the compact approximations to the derivatives terms by differentiating centrally the governing equations. Our compact scheme will approximate the derivative terms by involving the higher terms and reducing the number of grid points. The compact finite difference scheme is given for general form of the Goursat problem in uniform domain and illustrates the performance by applying a linear problem. Numerical experiments have been conducted with the new scheme and encouraging results have been obtained. In this paper we present the compact finite difference scheme for the Goursat problem. With the aid of computational software the scheme was programmed for determining the relative errors of linear Goursat problem.

Item Type:Article
Keywords:Compact finite difference; consistency; convergence; Goursat problem; stability
Journal:Sains Malaysiana
ID Code:5977
Deposited By: ms aida -
Deposited On:20 Feb 2013 03:37
Last Modified:14 Dec 2016 06:40

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