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

Journal Contribution - Journal Article

We consider the Modified CraigSneyd (MCS) scheme which forms a prominent time stepping method of the Alternating Direction Implicit type for multidimensional time-dependent convectiondiffusion equations with mixed spatial derivative terms. Such equations arise often, notably, in the field of financial mathematics. In this paper a first convergence theorem for the MCS scheme is proved where the obtained bound on the global temporal discretization errors has the essential property that it is independent of the (arbitrarily small) spatial mesh width from the semidiscretization. The obtained theorem is directly pertinent to two-dimensional convectiondiffusion equations with mixed derivative term. Numerical experiments are provided that illustrate our result.
Journal: Journal of Computational and Applied Mathematics
ISSN: 0377-0427
Volume: 296
Pages: 170 - 180
Publication year:2016