A new stability result for the modified Craig-Sneyd scheme applied to two-dimensional convection-diffusion equations with mixed derivatives

DOI10.1016/j.amc.2016.03.022zbMath1410.65319OpenAlexW2314642887MaRDI QIDQ1733474

Chittaranjan Mishra

Publication date: 21 March 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2016.03.022

zbMATH Keywords

initial-boundary value problemsconvection-diffusion equationsADI schemescomputational financevon Neumann stability analysis

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

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High-order ADI finite difference schemes for parabolic equations in the combination technique with application in finance ⋮ Highly efficient parallel algorithms for solving the Bates PIDE for pricing options on a GPU ⋮ ADI schemes for valuing European options under the Bates model ⋮ A Parallel Cyclic Reduction Algorithm for Pentadiagonal Systems with Application to a Convection-Dominated Heston PDE ⋮ A case study on pricing foreign exchange options using the modified Craig–Sneyd ADI scheme

Cites Work

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• Stability of the modified Craig-Sneyd scheme for two-dimensional convection-diffusion equations with mixed derivative term
• Stability of ADI schemes applied to convection--diffusion equations with mixed derivative terms
• Unconditional stability of second-order ADI schemes applied to multi-dimensional diffusion equations with mixed derivative terms
• An alternating-direction implicit scheme for parabolic equations with mixed derivatives
• Stochastic calculus for finance. II: Continuous-time models.
• Stability of ADI schemes for multidimensional diffusion equations with mixed derivative terms
• On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
• ADI Schemes for Pricing American Options under the Heston Model
• ADI finite difference schemes for option pricing in the Heston model with correlation

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