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The efficient numerical methods of the nonlinear parabolic integro-differential PDEs on unbounded spatial domains whose solutions blow up in finite time are considered. Based on the unified approach proposed in Zhang et al. (Phys Rev E 78:026709, 2008), Zhang et al. (Phys Rev E 79:046711, 2009), the nonlinear absorbing boundary conditions for one-dimensional and two-dimensional nonlinear parabolic...
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