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Numerical Methods for Partial Differential Equations pp 129–140Cite as

Convergence conditions of the explicit and weak implicit finite difference schemes for parabolic systems

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1297))

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References

  1. Zhou Yulin, Finite Difference Method of First Boundary Problem for Quasilinear Parabolic Systems, Scientia Sinica (Series A), Vol. XXVIII, NO.4 (1985), p368–385.

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  2. Shen Longjun et al., A Magnetohydrodynamic Numerical Method for a Laser-Irradiated Target, J. On Numerical Methods and Computer Applications, Vol.7, No.1 (1986), p1–7.

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  3. Tony F. Chan, Ding Lee, Longjun Shen, Stable Explicit Schemes for Equations of the Schrödinger Type, Research Report YALEU/DCS/RR-305, Yale Univ., March 1984. Also see SIAM j.Numer. Anal., Vol.23, No.2, April 1986.

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  4. Shen Longjun and Du yingyan, The Stability of the Finite Difference Solutions for a Class of Degenerate Parabolic Equations, J.Comp.Math., No.2 (1985). p175–187.

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  5. Li Deyuan, The Finite Difference Schemes for the System of Parabolic Equations in One Dimension, J. Comp. Math., No. 4 (1982), p.80-89.

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  6. Fu Hongyuan, Explicit Difference Schemes for Generalized Nonlinear Schrodinger System, Proceedings of the 1984 Beijing Symposium on Differential Geometry and Differential Equations, p153–158.

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  7. Chen Guangnan, Alternate Finite Difference Schemes for the System of Parabolic Equations in One Dimension, J. Comp. Math., No. 7 (1985), p164-174.

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, P.O.Box 8009, Beijing

    Long-jun Shen

Authors
  1. Long-jun Shen
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You-Ian Zhu Ben-yu Guo

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© 1987 Springer-Verlag

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Shen, Lj. (1987). Convergence conditions of the explicit and weak implicit finite difference schemes for parabolic systems. In: Zhu, YI., Guo, By. (eds) Numerical Methods for Partial Differential Equations. Lecture Notes in Mathematics, vol 1297. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078545

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  • DOI: https://doi.org/10.1007/BFb0078545

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18730-1

  • Online ISBN: 978-3-540-48126-3

  • eBook Packages: Springer Book Archive

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