ON A FINITE DIFFERENCE ANALOGUE OF AN ELLIPTIC BOUNDARY DIFFERENCE ANALOGUE OF AN ELLIPTIC BOUNDARY PROBLEM WHICH IS NEITHER DIAGONALLY DOMINANT NOR OF NON-NEGATIVE TYPE
Abstract
A study of a particular P(h4) finite difference analog of a two point boundary problem for the Sturm-Liouville equation is presented. This analog violates the usual properties of diagonal dominance and being of non-negative type at every interior mesh point. It is shown, however, that for the mesh size h taken sufficiently small a maximum principle is valid and that the discretization error is O(h4). It is further shown that the point Jacobi iteration method diverges while the forward-backward Gauss-Seidel method converges. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1962
- Accession Number
- AD0293887
Entities
People
- B.e. Hubbard
- J.h. Bramble
Organizations
- University of Maryland