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We present new high-order Alternating Direction Implicit (ADI) schemes forthe numerical solution of initial-boundary value problems forconvection-diffusion equations with mixed derivative terms. Our approach isbased on the unconditionally stable ADI scheme proposed by Hundsdorfer.Different numerical discretizations which lead to schemes which arefourth-order accurate in space and second-order accurate in time are discussed.

High-order ADI schemes for convection-diffusion equations with mixed derivative terms