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
edited Feb 3 at 18:08
Henrik Schumacher
58.6k581162
asked Feb 3 at 17:42
user3234456user3234456
164
$endgroup$
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
edited Feb 3 at 18:08
Henrik Schumacher
58.6k581162
asked Feb 3 at 17:42
user3234456user3234456
164
$endgroup$
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
edited Feb 3 at 18:08
Henrik Schumacher
58.6k581162
asked Feb 3 at 17:42
user3234456user3234456
164
$endgroup$
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
58.6k581162
asked Feb 3 at 17:42
user3234456user3234456
164
edited Feb 3 at 18:08
Henrik Schumacher
58.6k581162
asked Feb 3 at 17:42
user3234456user3234456
164
edited Feb 3 at 18:08
Henrik Schumacher
58.6k581162
edited Feb 3 at 18:08
Henrik Schumacher
58.6k581162
edited Feb 3 at 18:08
Henrik Schumacher
58.6k581162
58.6k581162
asked Feb 3 at 17:42
user3234456user3234456
164
asked Feb 3 at 17:42
user3234456user3234456
164
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])
answered Feb 3 at 22:19
Bill WattsBill Watts
3,6111621
$endgroup$
$begingroup$
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.
answered Feb 3 at 18:05
Henrik SchumacherHenrik Schumacher
58.6k581162
$endgroup$
$begingroup$
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 |
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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])
answered Feb 3 at 22:19
Bill WattsBill Watts
3,6111621
$endgroup$
$begingroup$
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])
answered Feb 3 at 22:19
Bill WattsBill Watts
3,6111621
$endgroup$
$begingroup$
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])
answered Feb 3 at 22:19
Bill WattsBill Watts
3,6111621
$endgroup$
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
3,6111621
answered Feb 3 at 22:19
Bill WattsBill Watts
3,6111621
answered Feb 3 at 22:19
Bill WattsBill Watts
3,6111621
answered Feb 3 at 22:19
Bill WattsBill Watts
3,6111621
3,6111621
$begingroup$
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.
answered Feb 3 at 18:05
Henrik SchumacherHenrik Schumacher
58.6k581162
$endgroup$
$begingroup$
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.
answered Feb 3 at 18:05
Henrik SchumacherHenrik Schumacher
58.6k581162
$endgroup$
$begingroup$
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.
answered Feb 3 at 18:05
Henrik SchumacherHenrik Schumacher
58.6k581162
$endgroup$
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.
answered Feb 3 at 18:05
Henrik SchumacherHenrik Schumacher
58.6k581162
edited Feb 3 at 18:13
answered Feb 3 at 18:05
Henrik SchumacherHenrik Schumacher
58.6k581162
answered Feb 3 at 18:05
Henrik SchumacherHenrik Schumacher
58.6k581162
answered Feb 3 at 18:05
Henrik SchumacherHenrik Schumacher
58.6k581162
58.6k581162
$begingroup$
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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