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High-order compact ADI methods for parabolic equations. (English) Zbl 1121.65092
Summary: 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.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65F05 Direct numerical methods for linear systems and matrix inversion
35Q53 KdV equations (Korteweg-de Vries equations)
Software:
FDL3DI; SHALL 4
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References:
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