Numerical algorithms for semilinear parabolic equations with small parameter based on approximation of stochastic equations

DOI10.1090/S0025-5718-99-01134-5zbMath0935.35062OpenAlexW2153422610MaRDI QIDQ4700196

M. V. Tretyakov, Grigori N. Milstein

Publication date: 1 November 1999

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-99-01134-5

zbMATH Keywords

reaction-diffusion equationBurgers equation with small viscositygeneralized KPP-equation with a small parameterspecial layer methodsstochastic differential equation with small noise

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Singular perturbations in context of PDEs (35B25) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Initial value problems for second-order parabolic equations (35K15)

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Cites Work

• Discretization and simulation of stochastic differential equations
• Multiple scale and singular perturbation methods
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• Solving Ordinary Differential Equations I
• The probability approach to numerical solution of nonlinear parabolic equations
• Functional Integration and Partial Differential Equations. (AM-109)
• Weak approximation of a diffusion process in a bounded domain
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• Adaptive Finite Element Methods for Parabolic Problems IV: Nonlinear Problems
• A stochastic particle method for the McKean-Vlasov and the Burgers equation
• A Method for the Numerical Calculation of Hydrodynamic Shocks
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