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A Generalized Peaceman–Rachford ADI Scheme for Solving Two-Dimensional Parabolic Differential Equations

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Abstract

A generalized Peaceman–Rachford alternating-direction implicit (ADI) scheme for solving two-dimensional parabolic differential equations has been developed based on the idea of regularized difference scheme. It is to be very well to simulate fast transient phenomena and to efficiently capture steady state solutions of parabolic differential equations. Numerical example is illustrated.

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REFERENCES

  • Dean J., and Glowinski, R. (1993). On some finite element methods for the numerical simulation of incompressible viscous flow. In Incompressible Computational Fluid Dynamics, Gunzburger, M. D., and Nicolaides, R. A., (Eds.), Cambridge, University Press.

    Google Scholar 

  • Douglas, J., and Rachford, H. (1956). On the numerical solution of the heat conduction problem in two and three space variables, Trans. Amer. Math. Soc. 82, 421–439.

    Google Scholar 

  • Glowinski, R. (1989). Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics, SIAM, Philadelphia.

    Google Scholar 

  • Glowinski, R. (1987). Le θ schema. In Numerical Methods for the Navier-Stokes Equations, Bristeau, M. O., Glowinski, R., and Perieux, J., (Eds.), Comp. Phy. Report 6, 73–187.

  • Kloucek, P., and Rys, F. S. (1994). Stability of the fractional step θ-scheme for the nonstationary Navier-Stokes equations, SIAM J. Num. Anal. 31, 1312–1335.

    Google Scholar 

  • Peaceman, D., and Rachford, M. (1955). The numerical solution of parabolic and elliptic differential equations, J. SIAM 3, 28–41.

    Google Scholar 

  • Samarskii, A. A., and Vabishchevich, P. N. (1994). Regularized difference schemes, MMCE 1, 44–50.

    Google Scholar 

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Dai, W. A Generalized Peaceman–Rachford ADI Scheme for Solving Two-Dimensional Parabolic Differential Equations. Journal of Scientific Computing 12, 353–360 (1997). https://doi.org/10.1023/A:1025631211217

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  • DOI: https://doi.org/10.1023/A:1025631211217

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