TY - JOUR
T1 - Numerical solution of blow-up problems for nonlinearwave equations on unbounded domains
AU - Brunner, Hermann
AU - Li, Hongwei
AU - Wu, Xiaonan
N1 - Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2013/9
Y1 - 2013/9
N2 - 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.
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.
KW - Absorbing boundary conditions
KW - Finite differencemethod
KW - Finite-time blow-up
KW - Nonlinear wave equation
KW - Unbounded domains
UR - http://www.scopus.com/inward/record.url?scp=84874614843&partnerID=8YFLogxK
U2 - 10.4208/cicp.160412.111012a
DO - 10.4208/cicp.160412.111012a
M3 - Journal article
AN - SCOPUS:84874614843
SN - 1815-2406
VL - 14
SP - 574
EP - 598
JO - Communications in Computational Physics
JF - Communications in Computational Physics
IS - 3
ER -