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The Three-Dimensional Partial Differential Equation with Constant Coefficients of Time-Delay of Alternating Direction Implicit Format

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In this paper, we consider the delay partial differential equation of three dimensions with constantcoefficients. We established the alternating direction difference scheme by the standard finite differencemethod, gave the order of convergence of the format and the expression of the difference scheme truncationerrors.

Abstract

In this paper, we consider the delay partial differential equation of three dimensions with constantcoefficients. We established the alternating direction difference scheme by the standard finite differencemethod, gave the order of convergence of the format and the expression of the difference scheme truncationerrors.

참고문헌 (12)

  1. R. Bellman, "Differential-Difference Equations" (1963), Academic Press
  2. Z. Z. Sun, "Numerical Methods for Partial Differential Equation" (2012), Science Press
  3. Y. Kuang, "Delay Differential Equations with Applications in Population Dynamics" (1993), Academic Press
  4. X. Lu, "Monotone method and convergence acceleration for finite-difference solution of parabolic problems with time delay", Numerical Methods for Partial Differential Equations, 11(6), pp.591~602 (1995)
  5. C. V. Pao, "Dynamics of a finite difference system of reaction diffusion equations with time delay", Journal of Difference Equations and Applications, 4(1), pp.1~11 (1998)
  6. C. V. Pao, "Finite difference reaction-diffusion systems with coupled boundary conditions and time delays", Journal of Mathematical Analysis and Applications, 272(2), pp.407~434 (2002)
  7. D. W. Peaceman, "The numerical solution of parabolic and elliptic differential equations", Journal of the Society for Industrial and Applied Mathematics, 3(1), pp.28~41 (1955)
  8. J. Douglas, "Alternating direction methods for three space variables", Numerische Mathematik, 4(1), pp.41~63 (1962)
  9. Z. Z. Sun, "Complicit alternating direction difference scheme for reaction diffusion equations", Computational Mathematics, 2(2), pp.209~224 (2004)
  10. X. Lu, "Combined iterative methods for numerical solutions of parabolic problems with time delays", Applied Mathematics and Computation, 89(1-3), pp.213~224 (1998)
  11. S. Jiang, "The difference method for the initial boundary value problem for the neutral delay differential equation", Journal of Shandong Normal University (Natural Science Edition), 17(1), pp.1~4 (2002)
  12. X. Liu, "A wavelet method for solving the delay differential equations", Journal of Lanzhou University (Natural Science Edition), 47, pp.87~90 (2011)

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