Stochastic Numerics for Mathematical Physics
Stochastic differential equations have many applications in the natural sciences. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce solution of multi-dimensional problems for partial differential equations to integration of stochasti...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2004, 2004
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| Edition: | 1st ed. 2004 |
| Series: | Scientific Computation
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Mean-square approximation for stochastic differential equations
- 2 Weak approximation for stochastic differential equations
- 3 Numerical methods for SDEs with small noise
- 4 Stochastic Hamiltonian systems and Langevin-type equations
- 5 Simulation of space and space-time bounded diffusions
- 6 Random walks for linear boundary value problems
- 7 Probabilistic approach to numerical solution of the Cauchy problem for nonlinear parabolic equations
- 8 Numerical solution of the nonlinear Dirichlet and Neumann problems based on the probabilistic approach
- 9 Application of stochastic numerics to models with stochastic resonance and to Brownian ratchets
- A Appendix: Practical guidance to implementation of the stochastic numerical methods
- A.1 Mean-square methods
- A.2 Weak methods and the Monte Carlo technique
- A.3 Algorithms for bounded diffusions
- A.4 Random walks for linear boundary value problems
- A.5 Nonlinear PDEs
- A.6 Miscellaneous
- References