Keller, Herbert B. (1971) A New Difference Scheme for Parabolic Problems. In: Numerical Solution of Partial Differential Equations–II. Academic Press , New York, NY, pp. 327-350. ISBN 978-0-12-358502-8. https://resolver.caltech.edu/CaltechAUTHORS:20170802-111549240
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Abstract
This chapter discusses a new difference scheme for parabolic mixed initial-boundary value problems in one space dimension. The scheme has a number of very desirable features. It is simple, easy to program, and efficient. It is unconditionally stable and has second order accuracy with nonuniform nets. Richardson or h → 0 extrapolation is valid and yields two orders of accuracy improvement per extrapolation (with nonuniform nets). It is A-stable as well, that is, if the exact solution decays in time, so does the numerical scheme, with approximately the same rate; the data, coefficients, and solution need only be piecewise smooth and all the above remain valid. The method is also applicable to parabolic systems, to nonlinear parabolic equations, and even to some hyperbolic systems with special properties. The chapter presents the method, indicates the error estimates, h → 0 extrapolation and discusses an efficient algorithm for its application to the problem.
| Item Type: | Book Section | |||||||||
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| Additional Information: | © 1971 Academic Press, Inc. Published by Elsevier Inc. This work was supported by the U. S. Army Research Office, Durham, under Contract DAHC 04-68-C-0006. | |||||||||
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| DOI: | 10.1016/B978-0-12-358502-8.50014-1 | |||||||||
| Record Number: | CaltechAUTHORS:20170802-111549240 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170802-111549240 | |||||||||
| Official Citation: | Herbert B. Keller, A NEW DIFFERENCE SCHEME FOR PARABOLIC PROBLEMS, In Numerical Solution of Partial Differential Equations–II, Academic Press, 1971, Pages 327-350, ISBN 9780123585028, https://doi.org/10.1016/B978-0-12-358502-8.50014-1. (http://www.sciencedirect.com/science/article/pii/B9780123585028500141) | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 79762 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 02 Aug 2017 18:34 | |||||||||
| Last Modified: | 15 Nov 2021 17:50 |
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