对差分法时程积分的反思

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基金项目: 国家自然科学基金

Rethinking to Finite Difference Time-Step Integrations

1.
Research Institue of Engineering Mechanics, Dalian Uinversity of Technology, Dalian 116023, P.R. China;
2.
Dept. Appl. Math., Mississippi State Univ., U. S. A.

摘要: 以往偏微分方程时间步的数值积分主要由有限差分法来执行,然而当时间步长较大时会引起数值不稳定性。本文给出的单点精细积分法导出的显式积分格式可证明是无条件稳定的。就扩散方程与对流─扩散方程作出了本文方法与差分法导出的格式之间的对比。数值例题也表明了单点积分法的优越性。
- 有限差分法 /
- 时间步积分 /
- 数值稳定性
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 singlepoint 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 employed in the present paper are made for diffusion and convective-diffusion equations. Nunierical examples show the superiority of the singlepoint integration method.
- finite difference method /
- time step integration /
- numerical stability

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[2]	O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, 4th ed. McGrawHill, NY(1991).
[3]	钟万勰,子域精细积分及偏微分方程数值解,计算结构力学及应用(待发表).
[4]	钟万勰等.《计算结构力学与最优控制》,大连理工大学出版社(1993).
[5]	W. X. Zhong and F. W. Williams, A precise time step integration method, Proc. Instn. Mech. Engrs., 208 (1994).

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