Abstract
The numerical time step integrations of PDEs are mainly carried out by the finite difference method to date. However, when the time step becomes longer, it causes the problem of numerical instability. The explicit integration schemes derived by the single point precise integration method given in this paper are proved unconditionally stable. Comparisons between the schemes derived by the finite difference method and the schemes by the method imployed in the present paper are made for diffusion and convective-diffusion equations. Numerical examples show the superiority of the single point integration method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
W. H. Press S. A. Teukolsky, W. T. Vettering and B. P. Flannery,Numerical Recipes in C, 2nd ed. Cambridge Univ. Press (1992).
O. C. Zienkiewicz and R. L. Taylor,The Finite Element Method, 4th ed. McGraw-Hill, NY (1991).
Zhong Wanxie, Subdomain precise integration method and numerical solution of partial differential equations,Computational Structural Mechanics and Its Applications. (in Chinese)
W. X. Zhong, et al..,Computational Structural Mechanics and Optimal Contro, Dalian University Press (1993). (in Chinese)
W. X. Zhong and F. W. Williams, A precise time step integration method,Proc. Instn. Mech. Engrs.,208 (1994).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wanxie, Z., Jianping, Z. Rethinking to finite difference time-step integrations. Appl Math Mech 16, 705–711 (1995). https://doi.org/10.1007/BF02453396
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02453396