The probability approach to numerical solution of nonlinear parabolic equations
- Milstein, Grigori N.
2010 Mathematics Subject Classification
- 60H10 60H30 65M99
- semilinear parabolicequations, reaction-diffusion systems, probabilistic representations for equations of mathematical physics, weak approximation of solutions of stochastic differential equations
A number of new layer methods for solving semilinear parabolic equations and reaction-diffusion systems is derived by using probabilistic representations of their solutions. These methods exploit the ideas of weak sense numerical integration of stochastic differential equations. In spite of the probabilistic nature these methods are nevertheless deterministic. A convergence theorem is proved. Some numerical tests are presented.
- Numerical Methods for Partial Differential equations, vol. 18 (2002), no.4, pp. 490-522.