Elliptic boundary value problems for the Helmholtz equation are considered in the paper. In order to estimate their solutions and also the gradient of the solution, a special probabilistic representation and a corresponding statistical algorithm are constructed. The algorithm is a version of the process of ‘walking over spheres and in balls’ for solving a system of local integral equations obtained from the original differential problem by using the central and noncentral Green functions for the Helmholtz operator in a ball.
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Russian Journal of Numerical Analysis and Mathematical Modelling
Editor-in-Chief: Dymnikov, Valentin P. / Kuznetsov, Yuri
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- Forthcoming Papers
- Random walks inside a domain for estimation of the gradient of solutions to elliptic boundary value problems
- Calculation of a 3D axial symmetric nonlinear wakefield
- Numerical simulation of flows of a heavy nonviscous fluid with a free surface in the gravity field over a bed surface with an arbitrary profile
- Asymptotic error estimate for general Newton-type methods and its application to differential equations
- Construction of 3D convex and weakly nonconvex hulls in problems of mathematical physics
- Extension of the algebraic aspect of the discrete maximum principle
Random walks inside a domain for estimation of the gradient of solutions to elliptic boundary value problems
A. V. Burmistrov
- Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia
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Published Online: 2008-01-27 | DOI: https://doi.org/10.1515/rnam.2007.026
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Published Online: 2008-01-27
Published in Print: 2007-12-01
Citation Information: Russian Journal of Numerical Analysis and Mathematical Modelling rnam, Volume 22, Issue 6, Pages 515–530, ISSN (Online) 1569-3988, ISSN (Print) 0927-6467, DOI: https://doi.org/10.1515/rnam.2007.026.
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- Forthcoming Papers
- Random walks inside a domain for estimation of the gradient of solutions to elliptic boundary value problems
- Calculation of a 3D axial symmetric nonlinear wakefield
- Numerical simulation of flows of a heavy nonviscous fluid with a free surface in the gravity field over a bed surface with an arbitrary profile
- Asymptotic error estimate for general Newton-type methods and its application to differential equations
- Construction of 3D convex and weakly nonconvex hulls in problems of mathematical physics
- Extension of the algebraic aspect of the discrete maximum principle
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