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, Jiwei, Houde Han, and Hermann Brunner. "Numerical Blow-up of Semilinear Parabolic PDEs on Unbounded Domains in a"e(2)." Journal of Scientific Computing 49.3 (2011): 367-382.