Mathematical Modeling & Simulation
HOME WORK # 1
Due Date: One week from date of distribution in the class.
1.1 Convert the following model into a standard form and identify its main features:
2
2
7.9
8.2
4.6
dt
yd
yy =−
; y(0) = 0., y(1) = 6.
1.2 Formulate the following model into a standard form and identify its main features:
q
x
q
dt
dx
q=−
1
; x(0) = 1.,
xz
dt
dq
q
=−+
2
1
; q(0) = 1.,
42
2
2=− xy
dt
zd
; z(0) = 1.,
1.3 Formulate the following model into a standard form and identify its main features:
x
dt
xd
dt
xd
dt
dx
xt 3015301530)3exp(15 2
2
3
3=−−++−−
;
with ,
0.0)0( =x0.1)0(
=
′
x, 1.0)0(
−
=
′
′
x, 40.14)9(
=
x.
1.4 Change this differential model into a standard form and find out its main features:
)(30tan85.1
3
xwx
dx
dy =−−
⎥
⎦
⎤
⎢
⎣
⎡
; with 0.0)0(
=
y
, 0.2)0(
=
′
y
,
and tabular form of w(x) is following:
x 0 10 20 30
w(x) 2 5 8 11
1.5 Re-formulate this partial differential equation based model into a standard form and
identify its main features:
)()1()1()1)(1()1( 2
2
2
2
xG
x
y
yby
x
y
cx
x
y
cxby
t
y
by +
∂
∂
+−
∂
∂
+=
∂
∂
++−
∂
∂
+
;
with given conditions.
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