论文信息 - Two-parameter, arbitrary order, exponential approximations for stiff equations

Two-parameter, arbitrary order, exponential approximations for stiff equations

A two-parameter family of approximations to the exponential function is considered. Constraints on the parameters are determined which guarantee the approximations are A-acceptable. The suitability of these approximations for 2-point A-stable exponential fitting is established. Several numerical methods, which produce these approximations when solving y' = Xy, are presented.

Zdenek Picel | Byron L. Ehle | B. L. Ehle | Z. Picel

[1] G. Dahlquist. A special stability problem for linear multistep methods , 1963 .

[2] Allan M. Krall,et al. The Root Locus Method , 1970 .

[3] Byron L. Ehle,et al. High order a-stable methods for the numerical solution of systems of D.E.'s , 1968 .

[4] J. Butcher. Implicit Runge-Kutta processes , 1964 .

[5] P. M. Hummel,et al. A Generalization of Taylor's Expansion , 1949 .

[6] J. D. Lawson. Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants , 1967 .

[7] Miss A.O. Penney. (b) , 1974, The New Yale Book of Quotations.

[8] R. K. Jain. Some A -Stable Methods for Stiff Ordinary Differential Equations , 1972 .

[9] B. L. Ehle. A-Stable Methods and Padé Approximations to the Exponential , 1973 .

[10] Theodore A. Bickart,et al. High order stiffly stable composite multistep methods for numerical integration of stiff differential equations , 1973 .

[11] R. Varga. On Higher Order Stable Implicit Methods for Solving Parabolic Partial Differential Equations , 1961 .

[12] H. A. Watts,et al. A-stable block implicit one-step methods , 1972 .

[13] F. Chipman. A-stable Runge-Kutta processes , 1971 .