Random Walks on Boundary for Solving PDEs
eBook - PDF

Random Walks on Boundary for Solving PDEs

  1. 141 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

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 Mathématiques & Équations différentielles. We have over one million books available in our catalogue for you to explore.

Information

Publisher
De Gruyter
Year
2013
Print ISBN
9783110628692
eBook ISBN
9783110942026
Edition
1
Topic
Mathématiques
Subtopic
Équations différentielles

Table of contents

  1. 1. Introduction
  2. 2. Random walk algorithms for solving integral equations
  3. 2.1. Conventional Monte Carlo scheme
  4. 2.2. Biased estimators
  5. 2.3. Linear-fractional transformations and relations to iterative processes
  6. 2.4. Asymptotically unbiased estimators based on singular approximation of the kernel
  7. 2.5. Integral equation of the first kind
  8. 3. Random Walk on Boundary algorithms for solving the Laplace equation
  9. 3.1. Newton potentials and boundary integral equations of the electrostatics
  10. 3.2. The interior Dirichlet problem and isotropic Random Walk on Boundary process
  11. 3.3. Solution of the Neumann problem
  12. 3.4. Random estimators for the exterior Dirichlet problem
  13. 3.5. Third boundary value problem and alternative methods of solving the Dirichlet problem
  14. 3.6. Inhomogeneous problems
  15. 3.7. Calculation of the derivatives near the boundary
  16. 3.8. Normal derivative of a double layer potential
  17. 4. Walk on Boundary algorithms for the heat equation
  18. 4.1. Heat potentials and Volterra boundary integral equations
  19. 4.2. Nonstationary Walk on Boundary process
  20. 4.3. The Dirichlet problem
  21. 4.4. The Neumann problem
  22. 4.5. Third boundary value problem
  23. 4.6. Unbiasedness and variance of the Walk on Boundary algorithms
  24. 4.7. The cost of the Walk on Boundary algorithms
  25. 4.8. Inhomogeneous heat equation
  26. 4.9. Calculation of derivatives on the boundary
  27. 5. Spatial problems of elasticity
  28. 5.1. Elastopotentials and systems of boundary integral equations of the elasticity theory
  29. 5.2. First boundary value problem and estimators for singular integrals
  30. 5.3. Other boundary value problems for the Lame equations and regular integral equations
  31. 6. Variants of the Random Walk on Boundary for solving the stationary potential problems
  32. 6.1. The Robin problem and the ergodic theorem
  33. 6.2. Stationary diffusion equation with absorption
  34. 6.3. Stabilization method
  35. 6.4. Multiply connected domains
  36. 7. Random Walk on Boundary in nonlinear problems
  37. 7.1. Nonlinear Poisson equation
  38. 7.2. Boundary value problem for the Navier-Stokes equation
  39. Bibliography