Numerical solution of the Neumann problem for nonlinear parabolic equations by probability approach
- Milstein, Grigori N.
- Tretyakov, Michael V.
2010 Mathematics Subject Classification
- 35K55 60H10 60H30 65M99
- Semilinear parabolic equations, Neumann problem, 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 the Neumann problem 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. 22 (2002), no. 4, pp. 599-622, under new title: A probabilistic approach to the solution of Neumann problem for nonlinear parabolic equations.