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Blowing up of a finite difference solution tou t = uxx + u2

Blowing up of a finite difference solution tou t = uxx + u2 This paper studies a finite difference approximation to the similinear heat equation (1) with special emphasis on the case when the exact solution blows up with the blowing-up timeT ∞. The key results will be given in Propositions 1 and 2. Proposition 1 states the local convergence, i.e., the convergence of the proposed finite difference solution to the exact solution in any fixed time interval 0 ⩽t ⩽ T, whereT < T ∞. Proposition 2 states the convergence of the numerical blowing-up time to the exact oneT ∞. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Blowing up of a finite difference solution tou t = uxx + u2

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References (10)

Publisher
Springer Journals
Copyright
Copyright © 1976 by Springer-Verlag New York Inc.
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/BF01448176
Publisher site
See Article on Publisher Site

Abstract

This paper studies a finite difference approximation to the similinear heat equation (1) with special emphasis on the case when the exact solution blows up with the blowing-up timeT ∞. The key results will be given in Propositions 1 and 2. Proposition 1 states the local convergence, i.e., the convergence of the proposed finite difference solution to the exact solution in any fixed time interval 0 ⩽t ⩽ T, whereT < T ∞. Proposition 2 states the convergence of the numerical blowing-up time to the exact oneT ∞.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Mar 26, 2005

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