Stuck on solving differential equation
$begingroup$
I have tried to solve :
$$begin{array}{l} Afrac{1}{r}frac{d}{{dr}}left(
{rfrac{{du}}{{dr}}} right) = - B + N{k^2}frac{{{I_0}left( {kr}
right)}}{{{I_0}left( {ka} right)}}\ BC:\ u(r) = a\
frac{{du}}{{dr}} = 0,,,at,,,,r = 0 end{array}$$
with
DSolve[A (1/r) D[r D[u[r], r], r] == -B + N k^2 (BesselI[0, k r]/ BesselI[0, a r]), u'[0] == 0, u[a] == 0, u[r], r]
but I didn't have any solution
differential-equations boundary-conditions
$endgroup$
add a comment |
$begingroup$
I have tried to solve :
$$begin{array}{l} Afrac{1}{r}frac{d}{{dr}}left(
{rfrac{{du}}{{dr}}} right) = - B + N{k^2}frac{{{I_0}left( {kr}
right)}}{{{I_0}left( {ka} right)}}\ BC:\ u(r) = a\
frac{{du}}{{dr}} = 0,,,at,,,,r = 0 end{array}$$
with
DSolve[A (1/r) D[r D[u[r], r], r] == -B + N k^2 (BesselI[0, k r]/ BesselI[0, a r]), u'[0] == 0, u[a] == 0, u[r], r]
but I didn't have any solution
differential-equations boundary-conditions
$endgroup$
add a comment |
$begingroup$
I have tried to solve :
$$begin{array}{l} Afrac{1}{r}frac{d}{{dr}}left(
{rfrac{{du}}{{dr}}} right) = - B + N{k^2}frac{{{I_0}left( {kr}
right)}}{{{I_0}left( {ka} right)}}\ BC:\ u(r) = a\
frac{{du}}{{dr}} = 0,,,at,,,,r = 0 end{array}$$
with
DSolve[A (1/r) D[r D[u[r], r], r] == -B + N k^2 (BesselI[0, k r]/ BesselI[0, a r]), u'[0] == 0, u[a] == 0, u[r], r]
but I didn't have any solution
differential-equations boundary-conditions
$endgroup$
I have tried to solve :
$$begin{array}{l} Afrac{1}{r}frac{d}{{dr}}left(
{rfrac{{du}}{{dr}}} right) = - B + N{k^2}frac{{{I_0}left( {kr}
right)}}{{{I_0}left( {ka} right)}}\ BC:\ u(r) = a\
frac{{du}}{{dr}} = 0,,,at,,,,r = 0 end{array}$$
with
DSolve[A (1/r) D[r D[u[r], r], r] == -B + N k^2 (BesselI[0, k r]/ BesselI[0, a r]), u'[0] == 0, u[a] == 0, u[r], r]
but I didn't have any solution
differential-equations boundary-conditions
differential-equations boundary-conditions
edited Feb 3 at 18:08
Henrik Schumacher
55.2k576154
55.2k576154
asked Feb 3 at 17:42
user3234456user3234456
164
164
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Fix your typo's to match your latex and we get a solution no problem.
ode = (A*D[r*D[u[r], r], r])/r == -B + (n*k^2*BesselI[0, k*r])/BesselI[0, k*a]
bc1 = u'[0] == 0
bc2 = u[a] == 0
DSolve[{ode, bc1, bc2}, u[r], r] // Flatten
{u[r] -> (
a^2 B BesselI[0, a k] - 4 n BesselI[0, Sqrt[a^2 k^2]] -
B r^2 BesselI[0, a k] + 4 n BesselI[0, Sqrt[k^2 r^2]])/(
4 A BesselI[0, a k])
$endgroup$
$begingroup$
first I thank you so much, second could you tell me where is my typo's? with many thanks
$endgroup$
– user3234456
Feb 4 at 4:24
$begingroup$
You haveBesselI[0,a r]
instead ofBesselI[0,k a]
in your code.
$endgroup$
– Bill Watts
Feb 4 at 4:38
add a comment |
$begingroup$
Chances are better with correct syntax. You missed a pair of braces ({ }
) around the equations. Moreover, N
is a built-in symbol, so I replaced it with n
. This is how the corrected code looks like:
DSolve[{
A (1/r) D[r D[u[r], r], r] == -B + n k^2 (BesselI[0, k r]/BesselI[0, a r]),
u'[0] == 0,
u[a] == 0
},
u[r],
r
]
However, it takes forwever to evaluate. This tells me that it is quite likely that no closed-form solution can be derived (under the given information). If you are interested only in a solution for concrete values of B
, k
, n
, and a
, you should first assign these values and use the numerical solver NDSolve
instead. Parameter studies can be performed with ParametricNDSolve
.
$endgroup$
$begingroup$
thanks for reply, unfortunately I need analytical solution only
$endgroup$
– user3234456
Feb 3 at 19:44
2
$begingroup$
BesselI[0, a r]
should be BesselI[0, k a]`.
$endgroup$
– bbgodfrey
Feb 3 at 22:25
add a comment |
Your Answer
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Fix your typo's to match your latex and we get a solution no problem.
ode = (A*D[r*D[u[r], r], r])/r == -B + (n*k^2*BesselI[0, k*r])/BesselI[0, k*a]
bc1 = u'[0] == 0
bc2 = u[a] == 0
DSolve[{ode, bc1, bc2}, u[r], r] // Flatten
{u[r] -> (
a^2 B BesselI[0, a k] - 4 n BesselI[0, Sqrt[a^2 k^2]] -
B r^2 BesselI[0, a k] + 4 n BesselI[0, Sqrt[k^2 r^2]])/(
4 A BesselI[0, a k])
$endgroup$
$begingroup$
first I thank you so much, second could you tell me where is my typo's? with many thanks
$endgroup$
– user3234456
Feb 4 at 4:24
$begingroup$
You haveBesselI[0,a r]
instead ofBesselI[0,k a]
in your code.
$endgroup$
– Bill Watts
Feb 4 at 4:38
add a comment |
$begingroup$
Fix your typo's to match your latex and we get a solution no problem.
ode = (A*D[r*D[u[r], r], r])/r == -B + (n*k^2*BesselI[0, k*r])/BesselI[0, k*a]
bc1 = u'[0] == 0
bc2 = u[a] == 0
DSolve[{ode, bc1, bc2}, u[r], r] // Flatten
{u[r] -> (
a^2 B BesselI[0, a k] - 4 n BesselI[0, Sqrt[a^2 k^2]] -
B r^2 BesselI[0, a k] + 4 n BesselI[0, Sqrt[k^2 r^2]])/(
4 A BesselI[0, a k])
$endgroup$
$begingroup$
first I thank you so much, second could you tell me where is my typo's? with many thanks
$endgroup$
– user3234456
Feb 4 at 4:24
$begingroup$
You haveBesselI[0,a r]
instead ofBesselI[0,k a]
in your code.
$endgroup$
– Bill Watts
Feb 4 at 4:38
add a comment |
$begingroup$
Fix your typo's to match your latex and we get a solution no problem.
ode = (A*D[r*D[u[r], r], r])/r == -B + (n*k^2*BesselI[0, k*r])/BesselI[0, k*a]
bc1 = u'[0] == 0
bc2 = u[a] == 0
DSolve[{ode, bc1, bc2}, u[r], r] // Flatten
{u[r] -> (
a^2 B BesselI[0, a k] - 4 n BesselI[0, Sqrt[a^2 k^2]] -
B r^2 BesselI[0, a k] + 4 n BesselI[0, Sqrt[k^2 r^2]])/(
4 A BesselI[0, a k])
$endgroup$
Fix your typo's to match your latex and we get a solution no problem.
ode = (A*D[r*D[u[r], r], r])/r == -B + (n*k^2*BesselI[0, k*r])/BesselI[0, k*a]
bc1 = u'[0] == 0
bc2 = u[a] == 0
DSolve[{ode, bc1, bc2}, u[r], r] // Flatten
{u[r] -> (
a^2 B BesselI[0, a k] - 4 n BesselI[0, Sqrt[a^2 k^2]] -
B r^2 BesselI[0, a k] + 4 n BesselI[0, Sqrt[k^2 r^2]])/(
4 A BesselI[0, a k])
answered Feb 3 at 22:19
Bill WattsBill Watts
3,4411620
3,4411620
$begingroup$
first I thank you so much, second could you tell me where is my typo's? with many thanks
$endgroup$
– user3234456
Feb 4 at 4:24
$begingroup$
You haveBesselI[0,a r]
instead ofBesselI[0,k a]
in your code.
$endgroup$
– Bill Watts
Feb 4 at 4:38
add a comment |
$begingroup$
first I thank you so much, second could you tell me where is my typo's? with many thanks
$endgroup$
– user3234456
Feb 4 at 4:24
$begingroup$
You haveBesselI[0,a r]
instead ofBesselI[0,k a]
in your code.
$endgroup$
– Bill Watts
Feb 4 at 4:38
$begingroup$
first I thank you so much, second could you tell me where is my typo's? with many thanks
$endgroup$
– user3234456
Feb 4 at 4:24
$begingroup$
first I thank you so much, second could you tell me where is my typo's? with many thanks
$endgroup$
– user3234456
Feb 4 at 4:24
$begingroup$
You have
BesselI[0,a r]
instead of BesselI[0,k a]
in your code.$endgroup$
– Bill Watts
Feb 4 at 4:38
$begingroup$
You have
BesselI[0,a r]
instead of BesselI[0,k a]
in your code.$endgroup$
– Bill Watts
Feb 4 at 4:38
add a comment |
$begingroup$
Chances are better with correct syntax. You missed a pair of braces ({ }
) around the equations. Moreover, N
is a built-in symbol, so I replaced it with n
. This is how the corrected code looks like:
DSolve[{
A (1/r) D[r D[u[r], r], r] == -B + n k^2 (BesselI[0, k r]/BesselI[0, a r]),
u'[0] == 0,
u[a] == 0
},
u[r],
r
]
However, it takes forwever to evaluate. This tells me that it is quite likely that no closed-form solution can be derived (under the given information). If you are interested only in a solution for concrete values of B
, k
, n
, and a
, you should first assign these values and use the numerical solver NDSolve
instead. Parameter studies can be performed with ParametricNDSolve
.
$endgroup$
$begingroup$
thanks for reply, unfortunately I need analytical solution only
$endgroup$
– user3234456
Feb 3 at 19:44
2
$begingroup$
BesselI[0, a r]
should be BesselI[0, k a]`.
$endgroup$
– bbgodfrey
Feb 3 at 22:25
add a comment |
$begingroup$
Chances are better with correct syntax. You missed a pair of braces ({ }
) around the equations. Moreover, N
is a built-in symbol, so I replaced it with n
. This is how the corrected code looks like:
DSolve[{
A (1/r) D[r D[u[r], r], r] == -B + n k^2 (BesselI[0, k r]/BesselI[0, a r]),
u'[0] == 0,
u[a] == 0
},
u[r],
r
]
However, it takes forwever to evaluate. This tells me that it is quite likely that no closed-form solution can be derived (under the given information). If you are interested only in a solution for concrete values of B
, k
, n
, and a
, you should first assign these values and use the numerical solver NDSolve
instead. Parameter studies can be performed with ParametricNDSolve
.
$endgroup$
$begingroup$
thanks for reply, unfortunately I need analytical solution only
$endgroup$
– user3234456
Feb 3 at 19:44
2
$begingroup$
BesselI[0, a r]
should be BesselI[0, k a]`.
$endgroup$
– bbgodfrey
Feb 3 at 22:25
add a comment |
$begingroup$
Chances are better with correct syntax. You missed a pair of braces ({ }
) around the equations. Moreover, N
is a built-in symbol, so I replaced it with n
. This is how the corrected code looks like:
DSolve[{
A (1/r) D[r D[u[r], r], r] == -B + n k^2 (BesselI[0, k r]/BesselI[0, a r]),
u'[0] == 0,
u[a] == 0
},
u[r],
r
]
However, it takes forwever to evaluate. This tells me that it is quite likely that no closed-form solution can be derived (under the given information). If you are interested only in a solution for concrete values of B
, k
, n
, and a
, you should first assign these values and use the numerical solver NDSolve
instead. Parameter studies can be performed with ParametricNDSolve
.
$endgroup$
Chances are better with correct syntax. You missed a pair of braces ({ }
) around the equations. Moreover, N
is a built-in symbol, so I replaced it with n
. This is how the corrected code looks like:
DSolve[{
A (1/r) D[r D[u[r], r], r] == -B + n k^2 (BesselI[0, k r]/BesselI[0, a r]),
u'[0] == 0,
u[a] == 0
},
u[r],
r
]
However, it takes forwever to evaluate. This tells me that it is quite likely that no closed-form solution can be derived (under the given information). If you are interested only in a solution for concrete values of B
, k
, n
, and a
, you should first assign these values and use the numerical solver NDSolve
instead. Parameter studies can be performed with ParametricNDSolve
.
edited Feb 3 at 18:13
answered Feb 3 at 18:05
Henrik SchumacherHenrik Schumacher
55.2k576154
55.2k576154
$begingroup$
thanks for reply, unfortunately I need analytical solution only
$endgroup$
– user3234456
Feb 3 at 19:44
2
$begingroup$
BesselI[0, a r]
should be BesselI[0, k a]`.
$endgroup$
– bbgodfrey
Feb 3 at 22:25
add a comment |
$begingroup$
thanks for reply, unfortunately I need analytical solution only
$endgroup$
– user3234456
Feb 3 at 19:44
2
$begingroup$
BesselI[0, a r]
should be BesselI[0, k a]`.
$endgroup$
– bbgodfrey
Feb 3 at 22:25
$begingroup$
thanks for reply, unfortunately I need analytical solution only
$endgroup$
– user3234456
Feb 3 at 19:44
$begingroup$
thanks for reply, unfortunately I need analytical solution only
$endgroup$
– user3234456
Feb 3 at 19:44
2
2
$begingroup$
BesselI[0, a r]
should be BesselI[0, k a]`.$endgroup$
– bbgodfrey
Feb 3 at 22:25
$begingroup$
BesselI[0, a r]
should be BesselI[0, k a]`.$endgroup$
– bbgodfrey
Feb 3 at 22:25
add a comment |
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