Published June 1978
| Published
Journal Article
Open
The Construction of Finite Difference Approximations to Ordinary Differential Equations
- Creators
- Doedel, Eusebius J.
Chicago
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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
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Additional details
- Eprint ID
- 32780
- Resolver ID
- CaltechAUTHORS:20120730-075654197
- National Research Council of Canada Postgraduate Scholarship
- Energy Research and Development Administration
- AT-04-3-767
- Created
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2012-07-30Created from EPrint's datestamp field
- Updated
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2019-10-03Created from EPrint's last_modified field