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High order ADI method for solving unsteady convection-diffusion problems. (English) Zbl 1053.65067
Summary: We propose a high order alternating direction implicit (ADI) solution method for solving unsteady convection-diffusion problems. The method is fourth order in space and second order in time. It permits multiple use of the one-dimensional tridiagonal algorithm with a considerable saving in computing time, and produces a very efficient solver. It is shown through a discrete Fourier analysis that the method is unconditionally stable for 2D problems. Numerical experiments are conducted to test its high accuracy and to compare it with the standard second-order Peaceman-Rachford ADI method and the spatial third-order compact scheme of B. J. Noye and H. H. Tan [Int. J. Numer. Methods Eng. 26, No. 7, 1615–1629 (1988; Zbl 0638.76104)].

65M06Finite difference methods (IVP of PDE)
35K15Second order parabolic equations, initial value problems
65M12Stability and convergence of numerical methods (IVP of PDE)