Numerical Blow-up of Semilinear Parabolic PDEs on Unbounded Domains in ℝ2

@article{Zhang2011NumericalBO,
  title={Numerical Blow-up of Semilinear Parabolic PDEs on Unbounded Domains in ℝ2},
  author={Jiwei Zhang and Houde Han and Hermann Brunner},
  journal={J. Sci. Comput.},
  year={2011},
  volume={49},
  pages={367-382}
}
We study the numerical solution of semilinear parabolic PDEs on unbounded spatial domains in R2 whose solutions blow up in finite time. Of particular interest are the cases where = R2 or is a sectorial domain in R2. 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… CONTINUE READING

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