Contractivity results for alternating direction schemes in Hilbert spaces
Applied Numerical Mathematics
Journal of Computational Physics
Fundamentals of Numerical Reservoir Simulation
Fundamentals of Numerical Reservoir Simulation
Time integration of the shallow water equations in spherical geometry
Journal of Computational Physics
On the contractivity of implicit-explicit linear multistep methods
Applied Numerical Mathematics
Accuracy and stability of splitting with stabilizing corrections
Applied Numerical Mathematics
Applied Numerical Mathematics
A velocity--diffusion method for a Lotka--Volterra system with nonlinear cross and self-diffusion
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
Fast resolution of a single factor Heath-Jarrow-Morton model with stochastic volatility
Journal of Computational and Applied Mathematics
A Contour Integral Method for the Black-Scholes and Heston Equations
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
Stability of ADI schemes for multidimensional diffusion equations with mixed derivative terms
Applied Numerical Mathematics
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We consider Alternating Direction Implicit (ADI) schemes for the numerical solution of initial-boundary value problems for convection-diffusion equations with cross derivative terms. We derive new linear stability results for three ADI schemes that have previously been studied in the literature. These results are subsequently used to show that the ADI schemes under consideration are unconditionally stable when applied to finite difference discretizations of general parabolic two-dimensional convection-diffusion equations. Supporting numerical evidence is included.