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Numerical Solution of Blow-Up Problems for Nonlinear Wave Equations on Unbounded Domains

Published online by Cambridge University Press:  03 June 2015

Hermann Brunner ,
Hongwei Li  and
Xiaonan Wu
Hermann Brunner*
Affiliation:
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C 5S7, Canada
Hongwei Li*
Affiliation:
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong College of Mathematical Sciences, Shandong Normal University, Jinan, 250014, P.R. China
Xiaonan Wu*
Affiliation:
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
*
Corresponding author.Email:[email protected]
Email:[email protected], [email protected]
Email:[email protected]
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Abstract

The numerical solution of blow-up problems for nonlinear wave equations on unbounded spatial domains is considered. Applying the unified approach, which is based on the operator splitting method, we construct the efficient nonlinear local absorbing boundary conditions for the nonlinear wave equation, and reduce the nonlinear problem on the unbounded spatial domain to an initial-boundary-value problem on a bounded domain. Then the finite difference method is used to solve the reduced problem on the bounded computational domain. Finally, a broad range of numerical examples are given to demonstrate the effectiveness and accuracy of our method, and some interesting propagation and behaviors of the blow-up problems for nonlinear wave equations are observed.

Keywords

65M0665M20Finite-time blow-upnonlinear wave equationabsorbing boundary conditionsfinite difference methodunbounded domains
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 3 , September 2013 , pp. 574 - 598
Copyright
Copyright © Global Science Press Limited 2013

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