Accession Number : AD0656902

Title :   NUMERICAL INVESTIGATION OF HIGHER ORDER DIFFERENCE METHODS FOR SOLVING ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS,

Corporate Author : NAVAL ORDNANCE LAB WHITE OAK MD

Personal Author(s) : Smith,Don R. ; Ullman,Frederick K.

Report Date : JUN 1967

Pagination or Media Count : 43

Abstract : The Dirichlet problem for the Poisson equation delta U = G in a domain D is considered. It has been thought in the past that the use of higher order difference schemes in the approximate solution of such problems is not practical. However, results due to Bramble and Hubbard show that when G is sufficiently smooth, a truncation error of O(h superscript 4) can be obtained by use of a difference scheme which is O(h superscript 4) in the interior but only O(h superscript 2) near the boundary, where h is the mesh spacing. Other results, due to Bramble, Hubbard, and Zlamal, give error estimates when the function G has an isolated singularity in D satisfying certain conditions. In this report, the approximate solution of the preceding Dirichlet problem is carried out for several functions G and for several domains D, with boundary values such that the solutions are known exactly. The difference schemes used are those for which error estimates were given by the preceding authors. The results show that these error estimates can be very useful in practice, and that it may be more economical in some cases to use a higher order difference scheme together with a larger value of the mesh spacing h. (Author)

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, *DIFFERENCE EQUATIONS), APPROXIMATION(MATHEMATICS), OPERATORS(MATHEMATICS), THEOREMS, INEQUALITIES, CONVERGENCE, NUMERICAL ANALYSIS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE