In this article we consider the Modified Craig–Sneyd (MCS) scheme which forms a prominent time-stepping method of the Alternating Direction Implicit type for. View the profiles of people named Craig Sneyd. Join Facebook to connect with Craig Sneyd and others you may know. Facebook gives people the power to. Craig Sneyd. /; People; /; Managers; /; Craig Sneyd. Find us at. ; Bella Vista Oval, Crown Tce, Bella Vista. Quicklinks. HFI · FNSW · Laws of the.
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In this article we consider the Modified Craig—Sneyd MCS scheme which forms a prominent time-stepping method of the Alternating Direction Implicit type for multidimensional time-dependent convection—diffusion equations with mixed spatial derivative terms. When the initial function is nonsmooth, which is often the case for example in financial mathematics, application of the MCS scheme can lead to spurious erratic behaviour of the numerical approximations.
We prove that this undesirable feature can be resolved by replacing the very first MCS timesteps by several sub steps of the implicit Euler scheme. This technique is often called Rannacher time stepping.
We derive a useful convergence bound for the MCS scheme combined with Rannacher time stepping when it is applied to a model two-dimensional convection—diffusion equation with mixed-derivative term and with Dirac-delta initial data.
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Ample numerical experiments are provided that show the sharpness of our obtained error bound. Most users should sign in with their email address. If you originally registered with a sjeyd please use that to sign in. To purchase short term access, please sign in to your Oxford Academic account above.
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Convergence analysis of the Modified Craig—Sneyd scheme for two-dimensional convection—diffusion equations with nonsmooth initial data Maarten Wyns. You do not currently have access to this article. You could not be signed in. Sign In Forgot password?
Mathematics > Numerical Analysis
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