Stochastic Methods for Boundary Value Problems : Numerics for High-dimensional PDEs and Applications.
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| Author / Creator: | Sabelfeld, Karl K. |
|---|---|
| Imprint: | Berlin/Boston, GERMANY : De Gruyter, 2016. ©2016 |
| Description: | 1 online resource (208) |
| Language: | English |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11408344 |
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| 100 | 1 | |a Sabelfeld, Karl K. | |
| 245 | 1 | 0 | |a Stochastic Methods for Boundary Value Problems : |b Numerics for High-dimensional PDEs and Applications. |
| 260 | |a Berlin/Boston, GERMANY : |b De Gruyter, |c 2016. | ||
| 264 | 4 | |c ©2016 | |
| 300 | |a 1 online resource (208) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 1 Introduction ; 2 Random walk algorithms for solving integral equations ; 2.1 Conventional Monte Carlo scheme ; 2.2 Biased estimators ; 2.3 Linear-fractional transformations and their relations to iterative processes. | |
| 505 | 8 | |a 2.4 Asymptotically unbiased estimators based on singular approximations 2.5 Integral equation of the first kind ; 3 Random walk-on-boundary algorithms for the Laplace equation ; 3.1 Newton potentials and boundary integral equations of the electrostatics. | |
| 505 | 8 | |a 3.2 The interior Dirichlet problem and isotropic random walk-on-boundary process 3.3 Solution of the Neumann problem ; 3.4 Random estimators for the exterior Dirichlet problem ; 3.5 Third BVP and alternative methods of solving the Dirichlet problem ; 3.6 Inhomogeneous problems. | |
| 505 | 8 | |a 3.7 Continuity BVP 3.7.1 Walk on boundary for the continuity problem ; 3.8 Calculation of the solution derivatives near the boundary ; 3.9 Normal derivative of a double-layer potential ; 4 Walk-on-boundary algorithms for the heat equation. | |
| 505 | 8 | |a 4.1 Heat potentials and Volterra boundary integral equations 4.2 Nonstationary walk-on-boundary process ; 4.3 The Dirichlet problem ; 4.4 The Neumann problem ; 4.5 Third BVP ; 4.6 Unbiasedness and variance of the walk-on-boundary algorithms. | |
| 504 | |a Includes bibliographical references. | ||
| 520 | |a This monograph is devoted to random walk based stochastic algorithms for solving high-dimensional boundary value problems of mathematical physics and chemistry. It includes Monte Carlo methods where the random walks live not only on the boundary, but also inside the domain. A variety of examples from capacitance calculations to electron dynamics in semiconductors are discussed to illustrate the viability of the approach. | ||
| 546 | |a In English. | ||
| 650 | 0 | |a Boundary value problems |x Numerical solutions. |0 http://id.loc.gov/authorities/subjects/sh85016105 | |
| 650 | 0 | |a Stochastic analysis. |0 http://id.loc.gov/authorities/subjects/sh85128175 | |
| 650 | 0 | |a Random walks (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85111357 | |
| 650 | 7 | |a MATHEMATICS |x Applied. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a Boundary value problems |x Numerical solutions. |2 fast |0 (OCoLC)fst00837129 | |
| 650 | 7 | |a Random walks (Mathematics) |2 fast |0 (OCoLC)fst01089818 | |
| 650 | 7 | |a Stochastic analysis. |2 fast |0 (OCoLC)fst01133499 | |
| 650 | 7 | |a Partielle Differentialgleichung |2 gnd |0 http://d-nb.info/gnd/4044779-0 | |
| 650 | 7 | |a Integralgleichung |2 gnd |0 http://d-nb.info/gnd/4027229-1 | |
| 650 | 7 | |a Randwertproblem |2 gnd |0 http://d-nb.info/gnd/4048395-2 | |
| 650 | 7 | |a Monte-Carlo-Simulation |2 gnd |0 http://d-nb.info/gnd/4240945-7 | |
| 650 | 7 | |a Irrfahrtsproblem |2 gnd |0 http://d-nb.info/gnd/4162442-7 | |
| 655 | 4 | |a Electronic books. | |
| 700 | 1 | |a Simonov, N. A. |0 http://id.loc.gov/authorities/names/n91005632 | |
| 776 | 0 | 8 | |i Print version: |z 9783110479065 |z 3110479060 |w (DLC) 2016042706 |w (OCoLC)949750711 |
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| 928 | |t Library of Congress classification |a QA379 |l Online |c UC-FullText |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=e000xna&AN=1362724 |z eBooks on EBSCOhost |g ebooks |i 12444040 | ||