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Stability of the modified Craig–Sneyd scheme for two-dimensional convection–diffusion equations with mixed derivative term

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  • in 't Hout, K.J.
  • Mishra, C.

Abstract

The modified Craig–Sneyd (MCS) scheme is a promising splitting scheme of the ADI type for multi-dimensional pure diffusion equations having mixed spatial-derivative terms. In this paper we investigate the extension of the MCS scheme to two-dimensional convection–diffusion equations with a mixed derivative. Both necessary and sufficient conditions on the parameter θ of the scheme are derived concerning unconditional stability in the von Neumann sense.

Suggested Citation

  • in 't Hout, K.J. & Mishra, C., 2011. "Stability of the modified Craig–Sneyd scheme for two-dimensional convection–diffusion equations with mixed derivative term," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(11), pages 2540-2548.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:11:p:2540-2548
    DOI: 10.1016/j.matcom.2011.04.004
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    Cited by:

    1. Maarten Wyns & Karel in 't Hout, 2016. "An adjoint method for the exact calibration of Stochastic Local Volatility models," Papers 1609.00232, arXiv.org.
    2. Karel in 't Hout & Pieter Lamotte, 2022. "Efficient numerical valuation of European options under the two-asset Kou jump-diffusion model," Papers 2207.10060, arXiv.org, revised May 2023.
    3. Karel in 't Hout & Jari Toivanen, 2015. "Application of Operator Splitting Methods in Finance," Papers 1504.01022, arXiv.org.
    4. Lynn Boen & Karel J. in 't Hout, 2019. "Operator splitting schemes for American options under the two-asset Merton jump-diffusion model," Papers 1912.06809, arXiv.org.
    5. Mishra, Chittaranjan, 2016. "A new stability result for the modified Craig–Sneyd scheme applied to two-dimensional convection–diffusion equations with mixed derivatives," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 41-50.

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