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```00100	THIS PROGRAM INTEGRATES UP TO FOUR FIRST-ORDER DIFFERENTIAL
00110	EQUATIONS BY THE FOURTH-ORDER RUNGE-KUTTA METHOD AND GIVES THE
00120	CHOICES OF SEEING A PRINTOUT OF THE INTEGRATED VALUE(S) AND
00130	THE PLOTTED FUNCTION(S).
00140
00150	THE START POINT, END POINT, AND THE SETPSIZE ARE ENTERED AS DATA
00160	ON LINE 100.
00170
00180	THE DIFFERENTIAL EQUATIONS ARE ENTERED ON LINE(S) 110 THRU 140
00190	INCLUSIVELY.
00200
00210	IN ORDER TO USE THE PROGRAM IT IS NECESSARY TO INCORPORATE THESE
00220	OR SIMILAR SUBSTITUTIONS:
00230
00240	     LET:  DX/DT=D(1)   AND   X=Y(1)
00250	           DY/DT=D(2)   AND   Y=Y(2)
00260	           DZ/DT=D(3)   AND   Z=Y(3)
00270
00280	AND SO ON FOR AS MANY AS FOUR VARIABLES.
00290	FOR EXAMPLE:
00300
00310	INTEGRATE THE FOLLOWING SYSTEM OF EQUATIONS
00320	           DX/DT=Y
00330	           DY/DT=-4X
00340	           DZ/DT=2Z
00350
00360	FROM T=0. TO T=2., WHERE THE INITIAL VALUES FOR X, Y, AND Z ARE
00370	0, 2, AND 1 RESPECTIVELY.
00380
00390	THE INPUT IS AS FOLLOWS:
00400
00410	     *100  DATA 0,2,.0625
00420	     *110  LET D(1)=Y(2)
00430	     *120  LET D(2)=-4*Y(1)
00440	     *130  LET D(3)=2*Y(3)
00450	     *RUN
00460
00470	WHEN THE PROGRAM IS IN THE PROCESS OF RUNNING IT WILL ASK FOR
00480	THE INITIAL GUESSES FOR THE AMOUNT OF VARIABLES GIVEN IN THE
00490	EQUATIONS.  IT GIVES THE OPTIONS OF VIEWING A PRINTOUT, A PLOT,
00500	OR BOTH.
00510
00520	THE CURRENT STEPSIZE IS PRINTED BEFORE THE PRINTOUT AND THE
00530	PLOT.  THE PROGRAM GIVES THE CHOICE OF CHANGING THE STEPSIZE.
00540
00550	AFTER THE OUTPUT HAS BEEN DISPLAYED THE PROGRAM CALCULATES A NEW
00560	START POINT, A NEW END POINT, AND SAVES THE LAST CALCULATED
00570	VALUES OF THE INTEGRATED FUNCTION(S) AS THE NEW INITIAL GUESSES.
00580	IT THEN GIVES THE CHOICE OF SEEING MORE OUTPUT STARTING AT THIS
00590	POINT.
00600
00610	END OF INSTRUCTIONS.

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