论文信息 - A unified set of single step algorithms. Part 1: General formulation and applications

A unified set of single step algorithms. Part 1: General formulation and applications

A general algorithm for a single step time marching scheme for use in dynamic or diffusion equations is presented. This algorithm is easily programmed in its universal form for all orders of approximation and covers most of the currently used schemes as well as presenting many new possibilities. In many cases it presents a computationally advantageous form over conventional procedures—this is particularly so when compared with the Newmark algorighm and its variants.

W. L. Wood | O. Zienkiewicz | R. Taylor | N. W. Hine

[1] O. C. Zienkiewicz,et al. An alpha modification of Newmark's method , 1980 .

[2] W. Liniger. Global accuracy and A-stability of one- and two-step integration formulae for stiff ordinary differential equations , 1969 .

[3] John C. Houbolt,et al. A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft , 1950 .

[4] W. L. Wood. A further look at Newmark, Houbolt, etc., time-stepping formulae , 1984 .

[5] O. C. Zienkiewicz,et al. An alternative single‐step algorithm for dynamic problems , 1980 .

[6] M. Lees,et al. A Linear Three-Level Difference Scheme for Quasilinear Parabolic Equations* , 1966 .

[7] J. Z. Zhu,et al. The finite element method , 1977 .

[8] O. C. Zienkiewicz. A new look at the newmark, houbolt and other time stepping formulas. A weighted residual approach , 1977 .

[9] W. L. Wood. On the Zienkiewicz three− and four−time−level schemes applied to the numerical integration of parabolic equations , 1978 .

[10] W. L. Wood. On the Zienkiewicz four‐time‐level scheme for the numerical integration of vibration problems , 1977 .

[11] O. C. Zienkiewicz,et al. Consistent use of finite elements in time and the performance of various recurrence schemes for the heat diffusion equation , 1981 .

[12] Edward L. Wilson,et al. A COMPUTER PROGRAM FOR THE DYNAMIC STRESS ANALYSIS OF UNDERGROUND STRUCTURES , 1968 .