Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published June 1978 | Published
Journal Article Open

The Construction of Finite Difference Approximations to Ordinary Differential Equations

Abstract

Finite difference approximations of the form Σ^(si)_(i=-rj)d_(j,i)u_(j+i)=Σ^(mj)_(i=1) e_(j,if)(z_(j,i)) for the numerical solution of linear nth order ordinary differential equations are analyzed. The order of these approximations is shown to be at least r_j + s_j + m_j - n, and higher for certain special choices of the points Z_(j,i). Similar approximations to initial or boundary conditions are also considered and the stability of the resulting schemes is investigated.

Additional Information

© 1978 Society for Industrial and Applied Mathematics. Received by the editors September 1, 1976, and in revised form March 21, 1977. This work was supported by the National Research Council of Canada under a Postgraduate Scholarship and by the U.S. Energy Research and Development Administration under Contract AT-04-3-767, Project Agreement 12. The author wishes to thank Professor J. M. Varah at the University of British Columbia for guiding the Ph.D. thesis upon which this paper is based. He is also thankful to the first referee for detailed suggestions concerning presentation and to the second referee for making the author aware of previous work by M. R. Osborne.

Attached Files

Published - DOEsiamjna78.pdf

Files

DOEsiamjna78.pdf
Files (1.3 MB)
Name Size Download all
md5:7db0a450c3fb927cf907120a63f8c0a7
1.3 MB Preview Download

Additional details

Created:
August 19, 2023
Modified:
October 18, 2023