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An efficient approach for solving a class of nonlinear \(2\text{D}\) parabolic PDEs. (English) Zbl 1065.35138
Summary: We consider a class of nonlinear \(2\)D parabolic equations that allow for an efficient application of an operator splitting technique and a suitable linearization of the discretized problem. We apply our scheme to study the finite extinction phenomenon for the porous-medium equation with strong absorption. A comparison of accuracy and computational efficiency of the resulting algorithms for several test problems is presented.

35K55 Nonlinear parabolic equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K65 Degenerate parabolic equations
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