Numerical solution of stiff and singularly perturbed boundary value problems with a segmented-adaptive formulation of the tau method

Authors:
P. Onumanyi and E. L. Ortiz

Journal:
Math. Comp. **43** (1984), 189-203

MSC:
Primary 65L10

DOI:
https://doi.org/10.1090/S0025-5718-1984-0744930-9

MathSciNet review:
744930

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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

DOI:
https://doi.org/10.1090/S0025-5718-1984-0744930-9

Keywords:
Initial value problems,
boundary value problems,
systems of ordinary differential equations,
stiff problems,
singularly perturbed problems,
step-by-step approximation,
adaptive methods,
Tau method

Article copyright:
© Copyright 1984
American Mathematical Society