A sharp error estimate for the numerical solution of multivariate Dirichlet problems

DOI10.1016/S0377-0427(96)00052-0zbMath0866.65069MaRDI QIDQ2564265

George A. Anastassiou, Alexander D. Bendikov

Publication date: 27 July 1997

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

zbMATH Keywords

convergenceDirichlet problemerror estimatesWiener processPoisson equationsimple random walkprobabilistic methods

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Brownian motion (60J65) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Probabilistic potential theory (60J45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06)

Cites Work

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• Quantitative extensions of the uniform boundedness principle
• A sharp error estimate for the numerical solution of a Dirichlet problem for the Poisson equation
• On the sharpness of error bounds in connection with finite difference schemes on uniform grids for boundary value problems of ordinary differential equations

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