论文信息 - Stability of collocation methods for the numerical solution ofy″=f (x,y)

Stability of collocation methods for the numerical solution ofy″=f (x,y)

The stability properties of the collocation methods using polynomials for the numerical solution ofy″=f(x,y) are studied in this paper. A simple procedure which can be used to determine the stability region of any method is presented. It is shown that all methods using points symmetrically placed in each subinterval are always stable at least in a finite interval. Some methods which have an infinite interval of stability are derived and their practical value is discussed.

L. Kramarz

[1] L. Kramarz. Global approximations to solutions of initial value problems , 1978 .

[2] Hermite methods for the numerical solution of ordinary initial value problems , 1979 .

[3] P. J. van der Houwen. Stabilized Runge–Kutta Methods for Second Order Differential Equations without First Derivatives , 1975 .

[4] K. Wright,et al. Some relationships between implicit Runge-Kutta, collocation and Lanczosτ methods, and their stability properties , 1970 .

[5] C. D. Boor,et al. Collocation at Gaussian Points , 1973 .