High-Order Compact ADI Methods for Parabolic Equations

Document Type



In this paper we develop a sixth-order compact scheme coupled with Alternating Direction Implicit (ADI) methods and apply it to parabolic equations in both 2-D and 3-D. Unconditional stability is proved for linear diffusion problems with periodic boundary conditions. Numerical examples supporting our theoretical analysis are provided.


Applied Mathematics | Engineering | Numerical Analysis and Computation | Ordinary Differential Equations and Applied Dynamics


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