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A sharp error estimate for the numerical solution of multivariate dirichlet problem

 

作者: George A. Anastassiou,   Alexander Bendikov,  

 

期刊: Stochastic Analysis and Applications  （Taylor Available online 1998）
卷期: Volume 16, issue 3  

页码: 403-422

 

ISSN:0736-2994

 

年代: 1998

 

DOI:10.1080/07362999808809542

 

出版商: Marcel Dekker, Inc.

 

关键词: Dirichlet Problem - Continuous and Discrete;Wiener Process and Simple Random Walk;Convergence With Rates;Second Modulus Of Continuity;Sharp Inequality;Approximate Solution;Average Operator;First Exit Time;Uniform Grid;Lipschitz Class;Arbitrary Domain

 

数据来源: Taylor

 

摘要:

For the multidimensional Dirichlet problem of the Poisson equation on an arbitrary compact domain, this study examines convergence properties with rates of approximate solutions, obtained by a standard difference scheme over inscribed uniform grids. Sharp quantitative estimates are given by the use of second moduli of continuity of the second single partial derivatives of the exact solution. This is achieved by employing the probabilistic method of simple random walk

 

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