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NDSolveValue
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Numerical Solution to the Telegraph Equation in 1D
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∂
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∂
2
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+
(
a
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b
)
∂
u
∂
t
-
2
c
2
∂
u
∂
2
x
+
a
b
u
=
0
o
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D
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n
[
1
]
:
=
a
=
0
.
7
;
b
=
0
.
6
;
c
=
1
.
1
;
Specify the initial condition:
I
n
[
2
]
:
=
f
[
x
_
]
=
D
[
0
.
1
2
5
E
r
f
[
(
x
-
0
.
5
)
/
0
.
1
2
5
]
,
x
]
;
P
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o
t
f
[
x
]
,
{
x
,
-
1
,
1
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,
.
.
.
O
u
t
[
2
]
=
Specify the initial speed:
I
n
[
3
]
:
=
v
I
n
i
t
[
x
_
]
=
-
c
*
D
[
f
[
x
]
,
x
]
-
(
a
+
b
)
f
[
x
]
/
2
;
P
l
o
t
v
I
n
i
t
[
x
]
,
{
x
,
-
1
,
1
}
,
.
.
.
O
u
t
[
3
]
=
Solve the equation:
I
n
[
4
]
:
=
u
i
f
=
N
D
S
o
l
v
e
V
a
l
u
e
[
{
D
[
u
[
t
,
x
]
,
{
t
,
2
}
]
+
(
a
+
b
)
D
[
u
[
t
,
x
]
,
{
t
,
1
}
]
-
2
c
D
[
u
[
t
,
x
]
,
{
x
,
2
}
]
+
a
b
u
[
t
,
x
]
0
,
u
[
0
,
x
]
f
[
x
]
,
D
e
r
i
v
a
t
i
v
e
[
1
,
0
]
[
u
]
[
0
,
x
]
v
I
n
i
t
[
x
]
,
D
i
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i
c
h
l
e
t
C
o
n
d
i
t
i
o
n
[
u
[
t
,
x
]
f
[
0
]
,
x
0
]
,
D
i
r
i
c
h
l
e
t
C
o
n
d
i
t
i
o
n
[
u
[
t
,
x
]
f
[
1
]
,
x
1
]
}
,
u
,
{
t
,
0
,
2
}
,
{
x
,
0
,
1
}
]
O
u
t
[
4
]
=
I
n
t
e
r
p
o
l
a
t
i
n
g
F
u
n
c
t
i
o
n
D
o
m
a
i
n
:
{
{
0
.
,
2
.
}
,
{
0
.
,
1
.
}
}
O
u
t
p
u
t
:
s
c
a
l
a
r
Visualize the solution:
I
n
[
5
]
:
=
P
l
o
t
3
D
u
i
f
[
t
,
x
]
,
{
x
,
0
,
1
}
,
{
t
,
0
,
2
}
,
O
u
t
[
5
]
=
Display the solution in a animation:
I
n
[
6
]
:
=
f
r
a
m
e
s
T
E
Q
=
T
a
b
l
e
P
l
o
t
u
i
f
[
t
,
x
]
,
{
x
,
0
,
1
}
,
,
{
t
,
0
,
2
,
0
.
1
}
;
F
r
a
m
e
L
i
s
t
V
i
d
e
o
[
f
r
a
m
e
s
T
E
Q
,
F
r
a
m
e
R
a
t
e
5
]
O
u
t
[
6
]
=
See Also
Solve Poisson's Equation Over an Interactively Changing Region
Related Symbols
NDSolveValue
DirichletCondition
Publisher Information
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