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ll
and
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e about Sharp PC-1500
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:/l
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SHARP
PROGRAM
T I
TL
E
I Outline I
FIRST
ORDER
DIFFERENT
IA
L EQUATION
PROGRAM NO.
PS
-
A-
7
CE-I
SO
required
Th
is program so
lv
es a first
order
differential equation by using
th
e Rung
c-
Kutt
a-
Gill method.
[ Operating Guide ]
<
Input>
Initial
co
nditions x
0
Yo
x value increme
nt
h
Solution interval
T
<O
u
tput
>
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 u
se
d for
th
e x
value progression.
In
PRO mode, modify
the
500
line equation as required.
Not
e:
Except for x = nh+x
0
(n=O
, I, 2.
---)a
proportional allocation
is
made for
they
value
be
twe
en x
0
+(n-
l)h
and
x
0
+nh.
[
Exa
mp
l
e]
I.
E
qua
tion
y'
= -
x.y
is
solvecl
u
ncl
er
the
in
it
ia
l conditi
on
of
x
0
= 0, provided Yo = I 0.
However, assuming h = 0.0 I, T = 0.03, y is obtained wi
th
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
th
e x value tak
en
in h increments, sequentially determine
Yn
of
they
value in Xn
= xo +
nh
(n=I,
2,
---).
Th
e formulas for
det
em1ining Xn+ 1 and Yn+ 1 from Xn and Yn are writt
en
as
fo
ll
ows, according
to
th
e Rungc
·Kutt
a-Gill
method.
y'
1
'=
y.
+ r1,
(j.1
=
<t
••
3r
1- (.l1) k..
k1
=
fi
j ( r . +
li
/ 2
,y
'
11
)
r2= ( 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,
Thu
s Y
n•
I has been determined from
Yn
. Here, n = 0, I, 2, -----
The
value
of
q
0
is 0 (zero) at the st
art
point x
0
,
and
q
4
is
thereafter taken as a
new
q
0
.
Do
not
sale this PDF !!! -
23
-
I
I·
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