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Boundary Value Techniques for Initial Value Problems in Ordinary Differential Equations

A. O. H. Axelsson and J. G. Verwer
Mathematics of Computation
Vol. 45, No. 171 (Jul., 1985), pp. 153-171
DOI: 10.2307/2008054
Stable URL: http://www.jstor.org/stable/2008054
Page Count: 19
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Boundary Value Techniques for Initial Value Problems in Ordinary Differential Equations
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Abstract

The numerical solution of initial value problems in ordinary differential equations by means of boundary value techniques is considered. We discuss a finite-difference method which was already investigated by Fox in 1954 and Fox and Mitchell in 1957. Hereby we concentrate on explaining the fundamentals of the method because for initial value problems the boundary value method seems to be fairly unknown. We further propose and discuss new Galerkin methods for initial value problems along the lines of the boundary value approach.

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