Convergence of the Modified Craig-Sneyd scheme for two-dimensional convection-diffusion equations with mixed derivative term

摘要

We consider the Modified Craig-Sneyd (MCS) scheme which forms a prominenttime stepping method of the Alternating Direction Implicit type formultidimensional time-dependent convection-diffusion equations with mixedspatial derivative terms. Such equations arise often, notably, in the field offinancial mathematics. In this paper a first convergence theorem for the MCSscheme is proved where the obtained bound on the global temporal discretizationerrors has the essential property that it is independent of the (arbitrarilysmall) spatial mesh width from the semidiscretization. The obtained theorem isdirectly pertinent to two-dimensional convection-diffusion equations with mixedderivative term. Numerical experiments are provided that illustrate our result.