Department of Mathematics
Numerical Blow-up of Semilinear Parabolic PDEs on Unbounded Domains in a"e(2)
We study the numerical solution of semilinear parabolic PDEs on unbounded spatial domains ω in R 2 whose solutions blow up in finite time. Of particular interest are the cases where ω = R 2 or ω is a sectorial domain in R 2. We derive the nonlinear absorbing boundary conditions for corresponding, suitably chosen computational domains and then employ a simple adaptive time-stepping scheme to compute the solution of the resulting system of semilinear ODEs. The theoretical results are illustrated by a broad range of numerical examples. © 2011 Springer Science+Business Media, LLC.
Adaptive time-stepping, Finite difference spatial discretization, Finite-time blow-up, Local nonlinear boundary conditions, Sectorial domains, Semilinear PDEs, Unbounded spatial domains
Source Publication Title
Journal of Scientific Computing
Link to Publisher's Edition
Zhang, J., Han, H., & Brunner, H. (2011). Numerical Blow-up of Semilinear Parabolic PDEs on Unbounded Domains in a"e(2). Journal of Scientific Computing, 49 (3), 367-382. https://doi.org/10.1007/s10915-011-9467-5