@Article{NMTMA-3-475, author = {}, title = {A Finite Difference Scheme for Blow-Up Solutions of Nonlinear Wave Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2010}, volume = {3}, number = {4}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2010.m88051}, url = {http://global-sci.org/intro/article_detail/nmtma/6010.html} }