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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Numerical solution of stiff and singularly perturbed boundary value problems with a segmented-adaptive formulation of the tau method
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by P. Onumanyi and E. L. Ortiz PDF
Math. Comp. 43 (1984), 189-203 Request permission

Abstract:

This paper concerns the application of Ortiz’ recursive formulation of the Tau method to the construction of piecewise polynomial approximations to the solution of linear and nonlinear boundary value problems for ordinary differential equations. A practical error estimation technique, related to the concept of correction in Zadunaisky’s sense, is considered and used in the design of an adaptive approach to the Tau method. It proves efficient in the numerical treatment of problems with rapid functional variations, stiff and singularly perturbed problems. A technique of increased accuracy at matching points of segmented Tau approximants is also discussed and successfully applied to several problems. Numerical examples show that, for a given degree of approximation, our segmented Tau approximant gives an accuracy comparable to that of the best segmented approximation of the exact solution by means of algebraic polynomials.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Math. Comp. 43 (1984), 189-203
  • MSC: Primary 65L10
  • DOI: https://doi.org/10.1090/S0025-5718-1984-0744930-9
  • MathSciNet review: 744930