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- 141 pages
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Random Walks on Boundary for Solving PDEs
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Yes, you can access Random Walks on Boundary for Solving PDEs by Karl K. Sabelfeld, Nikolai A. Simonov in PDF and/or ePUB format, as well as other popular books in Mathematics & Differential Equations. We have over one million books available in our catalogue for you to explore.
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Table of contents
- 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 relations to iterative processes
- 2.4. Asymptotically unbiased estimators based on singular approximation of the kernel
- 2.5. Integral equation of the first kind
- 3. Random Walk on Boundary algorithms for solving the Laplace equation
- 3.1. Newton potentials and boundary integral equations of the electrostatics
- 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 boundary value problem and alternative methods of solving the Dirichlet problem
- 3.6. Inhomogeneous problems
- 3.7. Calculation of the derivatives near the boundary
- 3.8. Normal derivative of a double layer potential
- 4. Walk on Boundary algorithms for the heat equation
- 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 boundary value problem
- 4.6. Unbiasedness and variance of the Walk on Boundary algorithms
- 4.7. The cost of the Walk on Boundary algorithms
- 4.8. Inhomogeneous heat equation
- 4.9. Calculation of derivatives on the boundary
- 5. Spatial problems of elasticity
- 5.1. Elastopotentials and systems of boundary integral equations of the elasticity theory
- 5.2. First boundary value problem and estimators for singular integrals
- 5.3. Other boundary value problems for the Lame equations and regular integral equations
- 6. Variants of the Random Walk on Boundary for solving the stationary potential problems
- 6.1. The Robin problem and the ergodic theorem
- 6.2. Stationary diffusion equation with absorption
- 6.3. Stabilization method
- 6.4. Multiply connected domains
- 7. Random Walk on Boundary in nonlinear problems
- 7.1. Nonlinear Poisson equation
- 7.2. Boundary value problem for the Navier-Stokes equation
- Bibliography