Hiroshima Mathematical Journal

A local Crank-Nicolson method for solving the heat equation

Abdurishit Abuduwali, Michio Sakakihara, and Hiroshi Niki

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Hiroshima Math. J. Volume 24, Number 1 (1994), 1-13.

First available in Project Euclid: 21 March 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 65M06: Finite difference methods
Secondary: 65M12: Stability and convergence of numerical methods


Abuduwali, Abdurishit; Sakakihara, Michio; Niki, Hiroshi. A local Crank-Nicolson method for solving the heat equation. Hiroshima Math. J. 24 (1994), no. 1, 1--13. https://projecteuclid.org/euclid.hmj/1206128130.

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  • [1] P. G. Ciarlet and J. L. Lions, Handbook of numerical analysis, North-Holland, 1990.
  • [2] J. D. Lawson and J. Li. Morris, The extrapolation of first order methods for parabolic partial differential equations, SIAM J. Num. Anal. 15 (1978), 1212-1225.
  • [3] A. R. Mitchell and D. F. Griffiths, The finite difference method in partial differential equations, John Wiley, New York, 1980.
  • [4] P. J. Roache, Computational Fluid Dynamics, Hermosa Publishers Inc., 1976.
  • [5] G. D. Smith, Numerical solution of partial differential equations, Oxford University Press, 1987.
  • [6] H. F. Trotter, On the product of semi-groups of operators, Proc. Amer. Math. Soc. 10 (1959) 545-551.
  • [7] N. Yajima and T. Nogi, Numerical analysis of evolution equations, Iwanami Press, 1977.