Institute of Computational Mathematics and Mathematical Geophysics

International Conference on Mathematical Methods in Geophysics «MMG-2003»

Akademgorodok, Novosibirsk, Russia, October 8-12, 2003

Abstracts

Stochastic modeling in geophysics and atmospheric physics

Numerical solving semilinear parabolic-type equations and forward backward stochastic differential equations

Makarov R.N.

Institute of Computational Mathematics and Mathematical Geophysics (Novosibirsk)

In the paper the task of numerical solving of FBSDEs and of connected Cauchy problem for semilinear second order equation of parabolic type is considered. Some layer approximation methods for solving the nonlinear Cauchy problem are proposed. They are derived by using probabilistic representation of the solutions, but be nevertheless deterministic. These methods allow to evaluate as the solutions as their gradient vectors. FBSDEs are solved by Euiler method on the basis of global approximation of the solution of the corresponded nonlinear problem.

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