A deterministic model for the distribution of the stopping time in a stochastic equation and its numerical solution

DOI10.1016/j.cam.2016.11.025zbMath1357.65012OpenAlexW2555166767MaRDI QIDQ507856

Jorge Eduardo Macías-Díaz, José Villa Morales

Publication date: 9 February 2017

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

Full work available at URL: https://doi.org/10.1016/j.cam.2016.11.025

zbMATH Keywords

monotonicitynumerical examplefinite difference methodboundednessBrownian motionstochastic differential equationsnonlinear partial differential equationsstochastic integral equationdiffusion-advection equationcracks on solidsfracture of materialsgeneralized exponential techniqueItô's stochastic integralParis' equationprobability distribution of hitting timeprobability-based numerical method

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) 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) Stochastic integral equations (60H20) Random integral equations (45R05)

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