Numerical solution of Dirichlet problems for nonlinear parabolic equations by probability approach
- Milstein, Grigori. N.
- Tretyakov, Michael V.
2010 Mathematics Subject Classification
- 35K55 60H10 60H30 65M99
- semilinear parabolic equations, Dirichlet problems, probabilistic representations for equations of mathematical physics, weak approximation of solutions of stochastic differential equations in bounded domain
A number of new layer methods solving Dirichlet problems for semilinear parabolic equations is constructed by using probabilistic representations of their solutions. The methods exploit the ideas of weak sense numerical integration of stochastic differential equations in bounded domain. In spite of the probabilistic nature these methods are nevertheless deterministic. Some convergence theorems are proved. Numerical tests are presented.
- IMA J. of Numerical Analysis, vol. 21 (2001), no. 4, pp. 887-917, under new title: Numerical solution of the Dirichlet problem for nonlinear parabolic equations by a probabilistic approach.