Abstract
Unbounded solutions (critical blow-up regimes) simulated by the 3D nonlinear diffusion equation in a spherical shell are studied. The coordinate splitting of the differential operator coupled with two spherical coordinate maps makes it possible to use periodic boundary conditions in the latitudinal and longitudinal directions and employ the computationally efficient Sherman-Morrison formula and Thomas algorithm. The resulting finite difference method is direct, with implicit and unconditionally stable schemes of second-order approximation in all the variables. Numerical tests demonstrate that it allows simulating different blow-up regimes in complex computational domains.
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