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The Construction of Finite Difference Approximations to Ordinary Differential Equations

Doedel, Eusebius J. (1978) The Construction of Finite Difference Approximations to Ordinary Differential Equations. SIAM Journal on Numerical Analysis, 15 (3). pp. 450-465. ISSN 0036-1429.

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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.

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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.
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National Research Council of Canada Postgraduate ScholarshipUNSPECIFIED
Energy Research and Development AdministrationAT-04-3-767
Issue or Number:3
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Official Citation:The Construction of Finite Difference Approximations to Ordinary Differential Equations Eusebius J. Doedel SIAM Journal on Numerical Analysis , Vol. 15, No. 3 (Jun., 1978), pp. 450-465
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32780
Deposited By: Ruth Sustaita
Deposited On:30 Jul 2012 17:00
Last Modified:03 Oct 2019 04:03

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