@Article{NMTMA-3-4,
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 = {<p style="text-align: justify;">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 &nbsp;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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2010.m88051},
url = {https://global-sci.com/article/90738/a-finite-difference-scheme-for-blow-up-solutions-of-nonlinear-wave-equations}
}