Numerical Blow-Up of Nonlinear Parabolic Integro-Differential Equations on Unbounded Domain
نویسندگان
چکیده
We study the numerical solution of semilinear parabolic integro-differential PDEs on unbounded spatial domains whose solutions blow up in finite time. We first introduce the unified approach to derive the nonlinear absorbing boundary conditions for one-dimensional and two-dimensional domains, then use the fixed point method to achieve a simple but efficient adaptive time-stepping scheme. The theoretical results are illustrated by a broad range of numerical examples, including a problem with a circle line blow-up. 2000 Mathematics Subject Classification: 65M06, 65L10, 35Q53, 35Q51.
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ورودعنوان ژورنال:
- J. Sci. Comput.
دوره 68 شماره
صفحات -
تاریخ انتشار 2016