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

DOI10.1016/j.amc.2017.12.034zbMath1428.60098arXiv1901.10039OpenAlexW2781558295MaRDI QIDQ2279241

Joshua Lee Padgett, Qin Sheng

Publication date: 12 December 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.10039

zbMATH Keywords

stabilitysplittingdegeneracynonuniform gridsquenching singularityKawarada equation

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Degenerate parabolic equations (35K65) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (14)

An exploration of a balanced up-downwind scheme for solving Heston volatility model equations on variable grids ⋮ An operator splitting approach for two-dimensional Kawarada problems ⋮ Adaptive ADI difference solution of quenching problems based on the 3D convection-reaction-diffusion equation ⋮ Analysis of an approximation to a fractional extension problem ⋮ A semi-adaptive preservative scheme for a fractional quenching convective-diffusion problem ⋮ An endeavor from the Glowinski-Le Tallec splitting for approximating the solution of Kawarada equation ⋮ Convergence of an Operator Splitting Scheme for Abstract Stochastic Evolution Equations ⋮ Quenching study of two-dimensional fractional reaction-diffusion equation from combustion process ⋮ Extremely low order time-fractional differential equation and application in combustion process ⋮ A preservative splitting approximation of the solution of a variable coefficient quenching problem ⋮ Adaptive high-order finite difference analysis of 2D quenching-type convection-reaction-diffusion equation ⋮ Second-order semi-discretized schemes for solving stochastic quenching models on arbitrary spatial grids ⋮ The quenching of solutions to time-space fractional Kawarada problems ⋮ Adaptive ADI numerical analysis of 2D quenching-type reaction: diffusion equation with convection term

Cites Work

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• A quenching criterion for a multi-dimensional parabolic problem due to a concentrated nonlinear source
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• On solutions of initial -boundary problem for \(u_t=u_{xx}+1/(1-u)\)
• An adaptive Rothe method for nonlinear reaction-diffusion systems
• Parabolic quenching for nonsmooth convex domains
• Mathematical problems from combustion theory
• Quenching, nonquenching, and beyond quenching for solution of some parabolic equations
• An adaptive splitting approach for the quenching solution of reaction-diffusion equations over nonuniform grids
• Nonlinear time-fractional differential equations in combustion science
• Channel flow of a viscous fluid in the boundary layer
• Chaos-free numerical solutions of reaction-diffusion equations
• The Quenching of Solutions of Some Nonlinear Parabolic Equations
• Global error estimates for exponential splitting
• Solving Degenerate Reaction-Diffusion Equations via Variable Step Peaceman--Rachford Splitting
• Nonuniform Crank‐Nicolson scheme for solving the stochastic Kawarada equation via arbitrary grids
• A Revisit of the Semi-Adaptive Method for Singular Degenerate Reaction-Diffusion Equations
• Remarks on quenching
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