On Stochastic Algorithms for Solving Boundary-Value Problems for the Laplace Operator

On Stochastic Algorithms for Solving Boundary-Value Problems for the Laplace Operator

The paper deals with the mixed boundary-value problem for the Poisson equation. Random walks inside the domain are constructed and unbiased estimators for the solution of the boundary-value problem are defined on their trajectories. The finiteness of the estimator variance is proved. The possibility...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2017-09, Vol.225 (5), p.812-817
1. Verfasser: Sipin, A. S.
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Analysis
Boundary value problems
Differential equations
Estimators
Mathematical analysis
Mathematics
Mathematics and Statistics
Monte Carlo methods
Monte Carlo simulation
Poisson equation
Random walk
Randomness
Trajectory analysis
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Zusammenfassung:The paper deals with the mixed boundary-value problem for the Poisson equation. Random walks inside the domain are constructed and unbiased estimators for the solution of the boundary-value problem are defined on their trajectories. The finiteness of the estimator variance is proved. The possibility of practical realization of the estimators by the Monte Carlo method is studied.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-017-3497-y