Approximate solution of boundary value problems on infinite intervals by collocation methods

Author:
Christian Schmeiser

Journal:
Math. Comp. **46** (1986), 479-490

MSC:
Primary 65L10; Secondary 34A10, 34B15

MathSciNet review:
829620

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Abstract: The numerical solution of boundary value problems for ordinary differential equations on infinite intervals is considered. The infinite interval is cut at a finite, large enough point and additional boundary conditions are posed there. For the solution of the resulting problem, *A*-stable symmetric collocation methods are employed. Using the behavior of the solution of the "infinite" problem, meshes are defined which avoid an unreasonably high number of meshpoints. Stability and convergence of the resulting schemes are shown.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1986-0829620-8

Keywords:
Nonlinear boundary value problems,
asymptotic properties,
difference equations,
stability of difference equations

Article copyright:
© Copyright 1986
American Mathematical Society