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A Finite Difference Scheme for Blow-Up Solutions of Nonlinear Wave Equations

A Finite Difference Scheme for Blow-Up Solutions of Nonlinear Wave Equations
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Year:    2010

Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 4 : pp. 475–498

Abstract

We consider a finite difference scheme for a nonlinear wave equation, whose solutions may lose their smoothness in finite time, i.e., blow up in finite time. In order to numerically reproduce blow-up solutions, we propose a rule for a time-stepping, which is a variant of what was successfully used in the case of nonlinear parabolic equations. A  numerical blow-up time is defined and is proved to converge, under a certain hypothesis, to the real blow-up time as the grid size tends to zero.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2010.m88051

Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 4 : pp. 475–498

Published online:    2010-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Finite difference method nonlinear wave equation blow-up.

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