Volume 14, Issue 3
Numerical Solution of Blow-up Problems for Nonlinear Wave Equations on Unbounded Domains

Hermann Brunner, Hongwei Li & Xiaonan Wu

Commun. Comput. Phys., 14 (2013), pp. 574-598.

Published online: 2013-09

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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.


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@Article{CiCP-14-574, author = {Hermann Brunner, Hongwei Li and Xiaonan Wu}, title = {Numerical Solution of Blow-up Problems for Nonlinear Wave Equations on Unbounded Domains}, journal = {Communications in Computational Physics}, year = {2013}, volume = {14}, number = {3}, pages = {574--598}, 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.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.160412.111012a}, url = {http://global-sci.org/intro/article_detail/cicp/7173.html} }
TY - JOUR T1 - Numerical Solution of Blow-up Problems for Nonlinear Wave Equations on Unbounded Domains AU - Hermann Brunner, Hongwei Li & Xiaonan Wu JO - Communications in Computational Physics VL - 3 SP - 574 EP - 598 PY - 2013 DA - 2013/09 SN - 14 DO - http://dor.org/10.4208/cicp.160412.111012a UR - https://global-sci.org/intro/cicp/7173.html KW - AB -

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.


Hermann Brunner, Hongwei Li & Xiaonan Wu. (1970). Numerical Solution of Blow-up Problems for Nonlinear Wave Equations on Unbounded Domains. Communications in Computational Physics. 14 (3). 574-598. doi:10.4208/cicp.160412.111012a
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