Numerical solution of degenerate stochastic Kawarada equations via a semi-discretized approach

Joshua L. Padgett and Qin Sheng

Applied Mathematics and Computation, 2018, vol. 325, issue C, 210-226

Abstract: 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.

Keywords: Kawarada equation; Quenching singularity; Degeneracy; Nonuniform grids; Splitting; Stability (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:325:y:2018:i:c:p:210-226

DOI: 10.1016/j.amc.2017.12.034

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