Numerical solution of degenerate stochastic Kawarada equations via a semi-discretized approach. (English) Zbl 1428.60098
Summary: The numerical solution of a highly nonlinear two-dimensional degenerate stochastic Kawarada equation is investigated. A semi-discretized approximation in space is comprised on arbitrary nonuniform grids. Exponential splitting strategies are then applied to advance solutions of the semi-discretized scheme over adaptive grids in time. It is shown that key quenching solution features including the positivity and monotonicity are well preserved under modest restrictions. The numerical stability of the underlying splitting method is also maintained without any additional restriction. Computational experiments are provided to not only illustrate our results, but also provide further insights into the global nonlinear convergence of the numerical solution.
MSC:
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 35K57 | Reaction-diffusion equations |
| 35K65 | Degenerate parabolic equations |
| 65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
| 65C30 | Numerical solutions to stochastic differential and integral equations |
Keywords:
Kawarada equation; quenching singularity; degeneracy; nonuniform grids; splitting; stabilityReferences:
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