A numerical algorithm for blow-up problems revisited

In many evolution equations, solutions may become unbounded in finite time. This phenomenon is often called blow-up and the finite time is called the blow-up time. To numerically reproduce the finite-time blow-up phenomenon, schemes with adaptive time meshes were considered to be necessary. Since th...

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Bibliographic Details
Published in:Numerical algorithms 2017-07, Vol.75 (3), p.675-697
Main Author: Cho, C.-H.
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Approximation
Computation
Computer Science
Norms
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
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Summary:In many evolution equations, solutions may become unbounded in finite time. This phenomenon is often called blow-up and the finite time is called the blow-up time. To numerically reproduce the finite-time blow-up phenomenon, schemes with adaptive time meshes were considered to be necessary. Since the numerical blow-up time is defined by an infinite sum, which implies that one needs to compute infinite times to achieve blow-up, this method cannot be carried out in real computation. As a consequence, Cho (Jpn. J. Indust. Appl. Math. 30 , 331–349 2013 ) proposed an algorithm accomplished by schemes with uniform time meshes for the computation of blow-up solutions. In this paper, we are concerned with a question: to what extent can this algorithm be applied to compute the blow-up solutions and reproduce the blow-up behavior?
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-016-0216-6