One-step piecewise polynomial multiple collocation methods for initial value problems

Author:
J. P. Hennart

Journal:
Math. Comp. **31** (1977), 24-36

MSC:
Primary 65L05

DOI:
https://doi.org/10.1090/S0025-5718-1977-0431686-9

MathSciNet review:
0431686

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Abstract | References | Similar Articles | Additional Information

Abstract: New methods are proposed for the numerical solution of systems of first-order differential equations. On each subinterval of a given mesh of size *h*, a polynomial of degree *l* is constructed, its parameters being determined by a multiple collocation technique. The resulting piecewise polynomial approximation is of order at the mesh points and between them. In addition, the *j*th derivatives of the approximation on each subinterval provide approximations of order , . Some of the methods proposed are shown to be *A*-stable or even strongly *A*-stable.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1977-0431686-9

Keywords:
Initial value problems,
ordinary differential equations,
piecewise polynomials,
collocation methods,
*A*-stability

Article copyright:
© Copyright 1977
American Mathematical Society