A probabilistic method for numerical solution of quasi-linear parabolic equations

摘要

Based on the work of Milstein [G.N. Milstein, The probability approach to numerical solution of nonlinear parabolic equations, Numer. Meth. Partial Differen. Equat. 18 (2002) 490–522] and Makarov [R.N. Makarov, Numerical solution of quasilinear parabolic equations and backward stochastic differential equations, Russ. J. Numer. Anal. Math. Modell. 18 (5) (2003) 397–412], we extend the layer method to be a more accurate numerical scheme than that Makarov used. Moreover, some convergence results of the obtained algorithms are proved. A numerical example is provided and the numerical results show that our scheme is much better than that used by Makarov.