D200: First-order Differential Equations (Runge-Kutta)

Author(s): G.A. Erskine	Library: MATHLIB
Submitter:	Submitted: 01.09.1983
Language: Fortran	Revised: 01.03.1994

Subroutine subprograms RRKSTP and DRKSTP advance the solution of the system of simultaneous first-order differential equations

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

On CDC and Cray computers, the double-precision version DRKSTP is not available.

Structure:

SUBROUTINE subprograms
User Entry Names : RKSTP, DRKSTP
Obsolete User Entry Names : RKSTP RRKSTP
Files Referenced : Unit 6
External References: user-supplied SUBROUTINE subprogram

Usage:

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

    CALL tRKSTP(N,H,X,Y,SUB,W)

N

(INTEGER) Number n of equations.

H

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

X

(type according to t) 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 N. 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 3*N elements required as working-space.

The user-supplied subroutine SUB should be of the form

    SUBROUTINE SUB(X,Y,F)

where the variable X and the one-dimensional arrays Y(*) 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:

acts as do nothing.

References:

1. F.B. Hildebrand, Introduction to numerical analysis, (McGraw-Hill, New-York 1956) Sect. 6.16.