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decuslib20-02
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decus/20-0026/rk1.doc
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SUBROUTINE RK1
PURPOSE
INTEGRATES A FIRST ORDER DIFFERENTIAL EQUATION
DY/DX=FUN(X,Y) UP TO A SPECIFIED FINAL VALUE
USAGE
CALL RK1(FUN,HI,XI,YI,XF,YF,ANSX,ANSY,IER)
DESCRIPTION OF PARAMETERS
FUN -USER-SUPPLIED FUNCTION SUBPROGRAM WITH ARGUMENTS X,Y
WHICH GIVES DY/DX
HI -THE STEP SIZE
XI -INITIAL VALUE OF X
YI -INITIAL VALUE OF Y WHERE YI=Y(XI)
XF -FINAL VALUE OF X
YF -FINAL VALUE OF Y
ANSX-RESULTANT FINAL VALUE OF X
ANSY-RESULTANT FINAL VALUE OF Y
EITHER ANSX WILL EQUAL XF OR ANSY WILL EQUAL YF
DEPENDING ON WHICH IS REACHED FIRST
IER -ERROR CODE
IER=0 NO ERROR
IER=1 STEP SIZE IS ZERO
REMARKS
IF XI IS GREATER THAN XF, ANSX=XI AND ANSY=YI
IF H IS ZERO, IER IS SET TO ONE, ANSX IS SET TO XI, AND
ANSY IS SET TO ZERO
SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
FUN IS A TWO ARGUMENT FUNCTION SUBPROGRAM FURNISHED BY THE
USER. DY/DX=FUN (X,Y)
CALLING PROGRAM MUST HAVE FORTRAN EXTERNAL STATEMENT
CONTAINING NAMES OF FUNCTION SUBPROGRAMS LISTED IN CALL TO
RK1
METHOD
USES FOURTH ORDER RUNGE-KUTTA INTEGRATION PROCESS ON A
RECURSIVE BASIS AS SHOWN IN F.B. HILDEBRAND, 'INTRODUCTION
TO NUMERICAL ANALYSIS',MCGRAW-HILL,1956. PROCESS IS
TERMINATED AND FINAL VALUE ADJUSTED WHEN EITHER XF OR YF
IS REACHED.