D203: Second-order Differential Equations (Runge-Kutta-Nyström)

Author(s): K.S. Kölbig	Library: MATHLIB
Submitter:	Submitted: 07.06.1992
Language: Fortran	Revised: 01.12.1994

Subroutine subprograms RRKNYS and DRKNYS advance the solution of the system of simultaneous second-order differential equations

where , by a single step of length h in the independent variable x.

On computers other than CDC or Cray, only the double-precision version DRKNYS is available. On CDC and Cray computers, only the single-precision version RRKNYS is available.

Structure:

SUBROUTINE subprograms
User Entry Names : RRKNYS, DRKNYS
Obsolete User Entry Names: RKNYS RRKNYS
External References: User-supplied SUBROUTINE subprogram

Usage:

For (type REAL), (type DOUBLE PRECISION),

    CALL tRKNYS(N,H,X,Y,YP,SUB,W)

N

(INTEGER) Number n of equations.

H

(type according to t) The step-length h.

X

On entry, X must be equal to the initial value of the independent variable x. On exit, X is equal to x+h.

Y

(type according to t) One-dimensional array of length . On entry, , must contain . On exit, , contains approximate values .

YP

(type according to t) One-dimensional array of length . On entry, , must contain . On exit, , contains approximate values .

SUB

Name of a user-supplied SUBROUTINE subprogram, declared EXTERNAL in the calling program.

W

(type according to t) Array containing at least 6*N elements required as working-space.

The user-supplied subroutine SUB should be of the form

    SUBROUTINE SUB(X,Y,YP,F)

where the variable X and the one-dimensional arrays Y(*), YP(*) and F(*) are of type t. This subroutine must set

Method:

Using boldface quantities to denote vectors of length n, the computational sequence is as follows:

The error per step is proportional to .

Error handling:

For or , control is returned to the calling program without any change in Y or YP.

References:

1. L. Collatz, The numerical treatment of differential equations, (Springer-Verlag Berlin 1960) 537