an:04205918
Zbl 0729.65077
Barles, G.; Souganidis, P. E.
Convergence of approximation schemes for fully nonlinear second order equations
EN
Asymptotic Anal. 4, No. 3, 271-283 (1991).
00157258
1991
j
65N12 35J65 35K60 91A15 91A23
nonlinear second order equations; convergence; monotone, stable and consistent scheme; comparison principle; viscosity solution; stochastic differential games
Authors' summary: We present a simple, purely analytic method for proving the convergence of a wide class of approximation schemes to the solution of fully nonlinear second-order elliptic or parabolic partial differential equations. Roughly speaking, we prove that any monotone, stable and consistent scheme converges to the correct solution provided that there exists a comparison principle for the limiting equation. This method is based on the notion of viscosity solution of Crandall and Lions and it gives completely new results concerning the convergence of numerical schemes for stochastic differential games.
Michael Sever (Jerusalem)