Fundamentals of Numerical Reservoir Simulation
Fundamentals of Numerical Reservoir Simulation
Accuracy and stability of splitting with stabilizing corrections
Applied Numerical Mathematics
Stability of ADI schemes applied to convection-diffusion equations with mixed derivative terms
Applied Numerical Mathematics
Contractivity of domain decomposition splitting methods for nonlinear parabolic problems
Journal of Computational and Applied Mathematics
Locally linearized fractional step methods for nonlinear parabolic problems
Journal of Computational and Applied Mathematics
Mathematics and Computers in Simulation
ACM Transactions on Mathematical Software (TOMS)
Concurrency and Computation: Practice & Experience
Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models
Computational Economics
A new fourth-order numerical algorithm for a class of nonlinear wave equations
Applied Numerical Mathematics
Stability of ADI schemes for multidimensional diffusion equations with mixed derivative terms
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
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We consider the unconditional stability of second-order ADI schemes in the numerical solution of finite difference discretizations of multi-dimensional diffusion problems containing mixed spatial-derivative terms. We investigate an ADI scheme proposed by Craig and Sneyd, an ADI scheme that is a modified version thereof, and an ADI scheme introduced by Hundsdorfer and Verwer. Both sufficient and necessary conditions are derived on the parameters of each of these schemes for unconditional stability in the presence of mixed derivative terms. Our main result is that, under a mild condition on its parameter @q, the second-order Hundsdorfer and Verwer scheme is unconditionally stable when applied to semi-discretized diffusion problems with mixed derivative terms in arbitrary spatial dimensions k=2.