Browse > Article
http://dx.doi.org/10.3745/JIPS.04.0094

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

Chu, QianQian (Dept. of Mathematics, Yanbian University)
Jin, Yuanfeng (Dept. of Mathematics, Yanbian University)
Publication Information
Journal of Information Processing Systems / v.14, no.5, 2018 , pp. 1068-1074 More about this Journal
Abstract
In this paper, we consider the delay partial differential equation of three dimensions with constant coefficients. We established the alternating direction difference scheme by the standard finite difference method, gave the order of convergence of the format and the expression of the difference scheme truncation errors.
Keywords
Alternating Direction Implicit Format; Stability; Time-Delay; Partial Differential Equation; Three-Dimensional;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Y. Kuang, Delay Differential Equations with Applications in Population Dynamics. New York, NY: Academic Press, 1993.
2 X. Lu, "Monotone method and convergence acceleration for finite-difference solution of parabolic problems with time delay," Numerical Methods for Partial Differential Equations, vol. 11, no. 6, pp. 591-602, 1995.   DOI
3 C. V. Pao, "Dynamics of a finite difference system of reaction diffusion equations with time delay," Journal of Difference Equations and Applications, vol. 4, no. 1, pp. 1-11, 1998.   DOI
4 C. V. Pao, "Finite difference reaction-diffusion systems with coupled boundary conditions and time delays," Journal of Mathematical Analysis and Applications, vol. 272, no. 2, pp. 407-434, 2002.   DOI
5 D. W. Peaceman and H. H. Rachford, "The numerical solution of parabolic and elliptic differential equations," Journal of the Society for Industrial and Applied Mathematics, vol. 3, no. 1, pp. 28-41, 1955.   DOI
6 J. Douglas, "Alternating direction methods for three space variables," Numerische Mathematik, vol. 4, no. 1, pp. 41-63, 1962.   DOI
7 Z. Z. Sun and X. L. Li, "Complicit alternating direction difference scheme for reaction diffusion equations," Computational Mathematics, vol. 2, no. 2, pp. 209-224, 2004.
8 X. Lu, "Combined iterative methods for numerical solutions of parabolic problems with time delays," Applied Mathematics and Computation, vol. 89, no. 1-3, pp. 213-224, 1998.   DOI
9 S. Jiang, Y. Chang, and D. Xie, "The difference method for the initial boundary value problem for the neutral delay differential equation," Journal of Shandong Normal University (Natural Science Edition), vol. 17, no. 1, pp. 1-4, 2002.   DOI
10 X. Liu, Y. Zhou, and J. Zhou, "A wavelet method for solving the delay differential equations," Journal of Lanzhou University (Natural Science Edition), vol. 47, pp. 87-90, 2011.
11 Z. Z. Sun, Numerical Methods for Partial Differential Equation (Chinese Edition). Beijing: Science Press, 2012.
12 R. Bellman and K. L. Cooke, Differential-Difference Equations. New York, NY: Academic Press, 1963.