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Mathematics of Computation

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Boundary value techniques for initial value problems in ordinary differential equations

Authors: A. O. H. Axelsson and J. G. Verwer
Journal: Math. Comp. 45 (1985), 153-171, S1
MSC: Primary 65L10; Secondary 65L05
MathSciNet review: 790649
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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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Keywords: Numerical analysis, initial value problems for ordinary differential equations, stiffness, boundary value techniques
Article copyright: © Copyright 1985 American Mathematical Society