PHM 665 Numerical Analysis MASTER

1. AIN SHAI,IS,UNIVERSITY
FACULTY OF BNGINEERING
Electronics and communication Engineering Department
Course: Numerical Analysis (pHM 665)
Assignrnent #71: System of first order D.E
.,problerns
in pag e 107r,

2. ?c +r +tJ
l-tX -Z
X (.'z) I )Co- ? )
zb) --t
gL*) : (=
, h= o'
7-:
!I
J:
In,
ff,
I6,*C tE',
W -s.*Hi,"-A.
?* +) +-t
q?.*?*
Pc*,Jf)
3tr,1+
'E.n
q
Cn
bx
g
I-..*)--
b
T='fltt
u
t_
' *!! )J"' Z
, in+
d1
5"**s
=h?(t,. ,X n, T t
*hi*^.*-,r,Y..Y 1
' h
a(
"!;. rt ,d,',+ut-
= tr^3
tf.* ,{;,1, ,
* Vl + zrl z+ zrl t + V .f
r &Jr + ?1uJ7 + Adl+ d.l
hlt*,x.-,J.,) r,
! [&,r*ry, $,t*'. ,IJ+.) (*."t
)" / (fr. i..," ,x^i,,l ,r^"X)
{* r',
Ll ttr'n , lnrn.,g;ur) (
"
u
t
-l
'V3 'l
hX
^,
.-t*
V4_
._r-t^-!a
n
o
-I
J11
;
o.l
c'lc)
a -ir"L
&
t
/,"5 /
l.o{S 1
l. l:")I
n-It) |
i
tl
i,l
--1,'
:
llI
I
1_^
o
Cr, bl
o,a
ol
T v=xq
t"
| ''tt'
i o t?
; o- tc:i
1
1
',,, u- lLl2 )
';: h
.o.h
aS?
/a t a.. .)
t)- ( -/ ./Ja C/
'0,]q( ,
o",l-{_-
--,-*."--_*_t---
o,-1tftr-',t", ) (_
! l qi _'_r_-,_
t,
"-'"<( tzrr

3. {-D, } o-, rri - -l '- *-i=-!.-*---
io't7c,ti -.?Jrc: ,
il
i r, -'-).
itl-i-**-
'''q"t+lr-7,":_q4
?::?A?:t3?sl--
o.8z!
",jrli
.:'-i
:PId,-,riiturt r:Sg:_
I
I(
35!
o7'(
Lqd
TIL{
l
]t
I3'1
":*
3l
o-
o-
o-
o.t7a j
"
i.r+*,____%
a.zoLtl i
___l
o.z jg/
a?
. s'r
L-)
G
(n
(;

4. D z$*t'l'*3X -+
Fu,,r,)) :
It
* t +:gXJ
$+t=A n:x =
_L
Lr+
D
L)v
tt,x,t)
DYI r g.ft!r-- 5',* o'7e
* r?r-rnuoi b5, U, ?r^17t ?q).2
*lr'i lu,,"h2G",X...i^).l
x*q ,If%j
" z,?to!. ,x*t/-
#{f #frfr, =h ett oh,. ,.(*{4
.
, Xnrt , gf")yrn' =''li1(l**I,'; ,t," orI>,
I
-) -,
*..-rr'1 I
orl
'ta
frlt
+l
ut
tr
h/
iy
xh
+
.!l
)nt
o'ii
{""
.11
At4
I
-Y
{1
s
(4
I
.L'
't4
.(
"t ")
I
t
1r
It'
n
Lri
l''1
f*
I
nY
D
II
F
l^
),r i
" 11+
v
A.
=h
h
i
i,1
.
7n
.Vii
l* ?
;h
,'
1
-: i,1
'
rl
b
v,,
L;
a
e-:
'rq
Lt
e'
J,
'^).
ht$ , .'g
4n X,.
1'alt..tt,
ti
oos ,, iasl"tr 5l
rlrip:,r,e i )la25i 2 trulo'?rl l
' i .i i
o
o]
"p.33hS
a-7-
o'Q 3
o.q 3
c -?t L>, q
c .41s5
I't
itl!
o I ! t to't';i 1 l6f,i ozrLf4',
-31,{}l
]
rT(;; r.','ii;, t 'r . ;l t,, -
l ''"t I l.(''1
s.34r,
t-'11'l-

5. -- |-t
I
ni
ir---t
1
l_
o 1
i :::: i:"::::1"--:]}1.::yl oz3_1 r i;-;;,ir-- . r--.-*-**-"--- i--*-*-*:
.i, 1
o'l) il.lfot i 2qr
lii-:I a t5 i t'ru1
i z s)al i
or'. u
',e.tt,zj
r,srs3i o.8/614
I i -i r----.-L i- ,
l r's i , , iqll{ e ss,uv i, )1,r,i,lr,r',,o,,,,i, ,,l,i+ri,, r,n, -I i i i --: 'r i -'ri
I * , !' t!:::-[7-.:lt::ri" :y11 (a AnL,i o zry
I a'4,r2
z /-1Hzt=:_10,
/:,

6. ffi
; z+{f x-
It v'" 1
' $,?+
DX=
f>qgJ
) 7r"- t ./'- v = z
+{tzVO
Xn*, 'Xn* rYL
lnr, ? *tt'"*
""=U
,,+tl' t ?{3 +Vt
> LJ + ?'^) e -+'?,J a d**
nL -llGr,l^,j")
Pl =W|" (t, ,"')
v, = )rf (+*be rY,.*{?, ,hZ i
,Pz=hfr ( rt r r/ id
)
us
= hl G, rl"u,!.*? ,)J "Z)
ug=nt, r y' , /,,i
V,,
= hf (|,.,, , A*v-i ,/ntvrr)
ur,
l.? ( r1
U
r1 I,t /^t
)
xG) =o
x'{c) >l
b
F(t,t,) =
1t{,r')
1,,^J X(o.rr)
V.,= o ,?.
l
f,n
0
o.Ll
e'.!F:
c--Z (,rlO ,7tsu1
c z$11"t
l.zzz
il
:l
D,Ic L7t:i u'7139 -ctt!
o.t7
o.zq4
t'
?l
).t-rh{r
X1-- o'"113 b
vf -- t 5"l ,'"'Ut 5),

8. r l!t.@
l.,nJ X(o ,")
^= o -?.
X b) =-a
x'{cs > I
lr]
+t*l yx-
'Xn+ W
Lt, , f;'*
? Cn*
*;4'
:,
^J,,+tt. t ?{3 +Vt
;. r-Jr+?t)e+?JL*J**
0
F(t,r,) =
1({,r') 3 Z
ur",
l.? ( r/
Xn *,
u
dn+ l
DX=
f> *,
g '''l
U
r/ ri" "'? )
yl
r-)
l
f,n
-;
a 4 q8
o,5c Llz, o"113{
o.L{
*.*---..--J
o -! 9q',L)C
c-"27 (,rf
- o rLtj
- -Q I i.'.,?z!-Jr'_-v /.,
vl
o, zuul|,
o.zgqL'1hL
r'1
-t
I o'l!
i
in'-'
I
!
'i 0'L:
I
,.^-I--*-----"-'
(
l.v
I /'l'
I
I ")--f vt 6i,

9. v= [+ =n3 I a NY
: I
a- lTnr-'b
/- )1-?.,
o.l8zz7
I
o,t1
i
u.l,?sqlr",r ra7b.rr3o! t1
o.7i4t
=
*
=)
D .1ll o.( I
"i1-J__.
ri
!
?.!V!i o.e3cqj l.zr3 n8
-
il---]-_l_*----.---.>
-4^/,zc