Written by Robert Hodges

This program solves differential equations numerically 
using ;	Eulers method
	Mid-point Euler
	Improved Euler
	Runge-Kutta
If the differential is a function of both x and y, 
then it can be solved by;	Eulers method
				Mid-p [XY]
				Imprv. [XY]

Just enter the differential function in terms of X (and Y)
into Function Memory 6 and when asked;
1) X, Y, Starting values of x and y (the coordinates)
2) H, The step distance
3) The method to use.
				

"DIFFERENTIAL STUFF"
"f6"				{f6 denote F-Mem 6  this could 
"X"? -> X			be a program if no F-memories 
"Y"? -> Y			are available}	
"H"? -> H
"UNTILL X="? -> @
"1 EULERS METHOD"
"2 MID-POINT EUL"
"3 IMPROVED EUL"
"4 RUNGE-KUTTA"
"5 MID-P EUL [XY]"
"6 IMPRV.EUL [XY]"
Lbl 1
"WHICH ONE"? -> C
1=C => Goto 2
2=C => Goto 3
3=C => Goto 4
4=C => Goto 5
5=C => Goto 7
6=C => Goto 6
"TRY AGAIN"
Goto 1
Lbl 2
Y+H*f6 -> Y
X+H -> X
X>=@ => Y_			{>= means 'equal to or greater than}
Goto 2				{_ means that stoopid triangle on 
Lbl 3				the prog menu}	
X -> Z
Z+0.5*H -> X
Y+H*f6 -> Y
Z+H -> X
X>=@ => Y_
Goto 3
Lbl 4
X -> Z
f6 -> F
Z+H -> X
Y+H*0.5*(F+f6) -> Y
X>=@ => Y_
Goto 4
Lbl 5
X -> Z
f6 -> D
Z+H/2 -> X
f6 -> F
Y+H*(D+4E+F)/6 -> Y
X>=@ => Y_
Goto 5
Lbl 6
f6 -> D
Y -> C
Y+H*D -> Y
X+H -> X
C+0.5H*(D+f6) -> Y
X>=@ => Y_
Goto 6
Lbl 7
X -> Z
Y -> C
f6 -> D
Z+0.5H -> X
Y+0.5H*D -> Y
C+H*f6 -> Y
Z+H -> X
X>=@ => Y_
Goto 7

There are likely to be mistakes so if you find any, 
mail me at 

	casio@bayliss.demon.co.uk

and I will check the listing.