Numerical solution of the Robin problem of Laplace equations with a Feynman-Kac formula and reflecting Brownian motions

DOI10.1007/s10915-016-0184-yzbMath1352.65021arXiv1506.03385OpenAlexW1173716557MaRDI QIDQ334322

Wei Cai, Yijing Zhou

Publication date: 1 November 2016

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.03385

zbMATH Keywords

numerical resultsBrownian motionSkorokhod problemLaplace equationFeynman-Kac formulareflecting Brownian motionRobin boundary problemboundary local timewalk on spheres method

Mathematics Subject Classification ID

Brownian motion (60J65) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) 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)

Related Items (5)

A Parallel Iterative Probabilistic Method for Mixed Problems of Laplace Equations with the Feynman--Kac Formula of Killed Brownian Motions ⋮ Solving elliptic equations with Brownian motion: bias reduction and temporal difference learning ⋮ A path integral Monte Carlo (PIMC) method based on Feynman-Kac formula for electrical impedance tomography ⋮ The stochastic counterpart of conservation laws with heterogeneous conductivity fields: application to deterministic problems and uncertainty quantification ⋮ What is the fractional Laplacian? A comparative review with new results

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