roblesjonah_917869_53770480_HW10_2850
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School
Arizona State University *
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Course
MISC
Subject
Mathematics
Date
Nov 24, 2024
Type
Pages
9
Uploaded by BailiffPelican2900
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Use
Taylor
series
expansions
to
derive
a
forward
difference
scheme,
over
equally-spaced
points,
using
any
or
all
of
f;, fi.1,
fis2,
fir3
and
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that
approximates
df/dx?
(2"
derivative
at
x;)
to
order
(Ax?)
discretization
error.
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You
want
to
solve
the
foIIowmg
1s%-order
Initial
Value
Problem:
initial
condition
T(t
=0)
=
T,
=
30.
4
0.
(a)
Use
the
(single-step,
explicit)
Euler
method
to
solve
the
1%-order
IVP
dT
=
_£
4_3_
L
where
T
is
the
temperature
of
the
room
(in
°C),
and
t
is
time
(in
dt
18
45
300
minutes).
Solve
the
problem
over
the
range
t
=
[0,
40]
minutes,
T(0)=30
using
step
size
At
=
10
min
(i.e.
calculate
T;
at
t;
=0,
t;
=
10,
t,
=
20,
t;
=
30,
and
t,
=
40
minutes).
Show
all
your
work
in
table
form,
like
we
did
in
class,
showing
how
you
start
from
each
(t;
T;)
to
get
the
next
t,,;,
“slope/”,
and
T,,;.
Tw=THl
st
ot
v
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U5
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y
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300
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ook,
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161
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=LA
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TZ
724
7
1
4
U5
oy
T
(b)
Make
a
sketch
of
T;(t;)
(i.e.
draw
and
connect
the
5
dots),
and
comment
about
what
time
you
think
(if
ever!)
the
temperature
of
the
room
will
get
down
to
18°C.
()
T
1'\2
(OQ)YV\
Yeathes
%°
¢
belween
/Z/C)
S
G1nd
?)O
5.
f\’\y
5&/655
wWould
be
‘\’:1G
$€ceonds
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