2014/12/05 by Karel in ’t Hout, Hout, Karel in 't, Maarten Wyns +1 · 1 citation
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1412.1959
openalex publication_date 2014/12/05 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
We consider the Modified Craig-Sneyd (MCS) scheme which forms a prominent\ntime stepping method of the Alternating Direction Implicit type for\nmultidimensional time-dependent convection-diffusion equations with mixed\nspatial derivative terms. Such equations arise often, notably, in the field of\nfinancial mathematics. In this paper a first convergence theorem for the MCS\nscheme is proved where the obtained bound on the global temporal discretization\nerrors has the essential property that it is independent of the (arbitrarily\nsmall) spatial mesh width from the semidiscretization. The obtained theorem is\ndirectly pertinent to two-dimensional convection-diffusion equations with mixed\nderivative term. Numerical experiments are provided that illustrate our result.\n