ChBE 521
Homework 7
due Wednesday, November 11
1. How would you use finite differences to solve the boundary value problem
in spherical coordinates
d
dr
r
2
dc
(
r
)
dr
=
kc
(
r
)
subject to the boundary conditions
c
(1) = 1
,
dc
(0)
dr
= 0
.
Solve the problem using
N
= 100.
2. Using finite differences (
N
= 50), solve the partial differential equation
∂c
(
t, x
)
∂t
= 0
.
1
∂
2
c
(
t, x
)
∂x
2
+
c
(
t, x
)
(1 +
c
(
x, t
))
subject to the boundary conditions
c
(
t,
0) = 1
,
c
(
t,
1) = 2
,
and the initial condition
c
(0
, x
) = 0.
3. Using collocation (
N
= 10), solve the problem
∂c
(
t, x
)
∂t
= 0
.
1
∂
2
c
(
t, x
)
∂x
2
+
c
(
x, t
)
subject to the boundary conditions
∂c
(
t,
0)
∂x
= 0
,
∂c
(
t,
1)
∂x
= 0
,
and the initial condition
c
(0
, x
) = 1.
4. Using finite differences/CrankNicolson (
N
= 100) and Strang splitting,
solve the the partial differential equation
∂c
(
t, x, y
)
∂t
=
∂
2
c
(
t, x, y
)
∂x
2
+ 2
∂
2
c
(
t, x, y
)
∂y
2
subject to the boundary conditions
∂c
(
t,
0
, y
)
∂x
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 Spring '10
 ChrisRao
 pH, Boundary value problem, initial condition, Boundary conditions, Strang

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