Sharp PC-1500 Applications Manual page 29

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SHARP
PROGRAM
T I TL E
I
Outline
I
FIRST ORDER DIFFERENTIA L EQUAT ION
PROGRAM NO.
PS- A-7
CE-I SO required
This program solves a first order differential equa tion by using the Rungc-Kutta-
Gill
method.
[ Operating Guide ]
< Input>
Initial conditions
x
0
Yo
x value increment h
Solution interval
T
<Output >
Xo
Yo
h
x=x, , x
2 , ......
y value for x
Write the equation as a subroutine on line 500.
< Key Operation >
I
E•rE•
I
key is used for the
x
value progression.
In PRO mode, modify the 500 line equation as required.
Note: Except for x = nh+x
0
(n=O, I , 2. ---)a proportional allocation is made for
they value between x
0
+(n - l)h and x
0
+nh.
[ Example]
I. Equation
y'
=
- x.y
is solvecl uncler
the
initial condition of
x
0
=
0,
provided
Yo
=
I
0.
However, assuming h = 0.0 I , T = 0.03, y
is
obtained with
x
= 0.03 ,
0 .06 and so on.
[ Contents] (Formulas)
Assume that the equation is y' =
f
(x,
y), with its initial condition of
(x
0 ,
y
0 ) .
With
the
x
value taken in h incremen ts, sequentially determine
Yn
of they value in
Xn
= xo
+
nh (n=I, 2, ---) .
The formulas for dete m1ining
Xn+ 1
and
Yn+ 1
from
X n
and
Yn
are written as
foll ows, according to th e Rungc·Kutta-Gill method.
y '
1
'= y. + r 1, (j.1 = <t •• 3r1- (.l1)
k. .
k1 = fi j ( r . + li/ 2 ,y '
11
)
r 2= ( I
- /J?)(
k1 - <11),
y(2) ~
y '
1
'+
r z, q,
2
=
q. ,+
3
r,- (
J
- ,/,l?)
k
1 •
k z= hf ( x .
+
11/ 2 .y ' " )
r,•
( I
-/J?) (
k,-
q ,)
y )
=
y
1
+ , , .
q., =q,,+ 3r, -( J - / R) kt, k , = hj ( r . + J ,y
' )
, , _ ( l/ 6 )( k, - 2 q,)
Jl• - 1
=
y ' -
r._
q,=
q,,+
3
r, -
(1/ 2}
k ,
Thus Yn•
I
has been determined from Yn . Here, n
= 0,
I , 2, -----
The value of q
0
is 0 (zero) at the start poin t x
0
,
and
q
4
is thereafter taken
as
a
new q
0
.
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