Abstract
We study the numerical solution of semilinear parabolic PDEs on unbounded spatial domains ? in ?2 whose solutions blow up in finite time. Of particular interest are the cases where ?=?2 or ? is a sectorial domain in ?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.
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