Boundary Value Techniques for Initial Value Problems in Ordinary Differential Equations

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 fundament...

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Bibliographic Details
Published in:Mathematics of computation 1985, Vol.45 (171), p.153-171
Main Authors: Axelsson, A. O. H., Verwer, J. G.
Format: Article
Language:English
Subjects:
Approximation
Boundary value problems
Cauchy problem
Eigenvalues
Error rates
Exact sciences and technology
Galerkin methods
Mathematics
Midpoint rule
Numerical analysis
Numerical analysis. Scientific computation
Numerical integration
Ordinary differential equations
Sciences and techniques of general use
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Summary: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.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-1985-0790649-9