Timeline for Eigenvalue problem
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 23, 2014 at 5:49 | comment | added | Hossein Ebadi | Dear Micheal Many Thanks for your guide! Again the same problem remain! Is it possible to explain in detail? I am studying physics and I am not so professional in mathematics. | |
| Nov 23, 2014 at 4:09 | comment | added | Michael Renardy | Your equation becomes hypergeometric under the substitution $u=\exp(-\alpha z)$. | |
| Nov 22, 2014 at 19:41 | comment | added | Yoav Kallus | PS, I just noticed on Wikipedia a link to the Lehmer-Schur algorithm which is described as an extension of the bisection method to the complex plane. I don't know anything about it, but you should check if it does what you want. | |
| Nov 22, 2014 at 19:39 | comment | added | Yoav Kallus | I think you can still use the shooting method, but instead of a bracketing root finding method (like bisection method), you will have to use a method that doesn't rely on bracketing. I think you could even use Newton's method, since you can write down $dy(1)/d\omega$ as an integral that you can evaluate numerically. | |
| Nov 22, 2014 at 19:32 | comment | added | Hossein Ebadi | Dear Yoav I need only the walues of w1 and w2. Maybe I plot w1/w2 with respect to some values of m and alpha. The i symbol is confusing me. without it, it is possible to solve it by shooting method! I will check in the same way as you described. | |
| Nov 22, 2014 at 18:50 | comment | added | Yoav Kallus | Since you have numeric values for your constants $h$, $m$, and $\alpha$, would you be satisfied with numerical results? If so, You could write $y(z)=\sum_{k=1}^\infty a_k \sin(k \pi z)$, and convert your eigenvalue problem to a discrete one in terms of the $a_k$'s. To solve it numerically, just truncate the sum at some sufficiently high value $1\le k \le M$. | |
| Nov 22, 2014 at 17:01 | history | edited | Hossein Ebadi | CC BY-SA 3.0 |
added 12 characters in body
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| Nov 22, 2014 at 16:59 | history | edited | Ben McKay | CC BY-SA 3.0 |
spelling, grammar, maths
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| Nov 22, 2014 at 16:41 | history | edited | Hossein Ebadi | CC BY-SA 3.0 |
added 35 characters in body
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| Nov 22, 2014 at 16:13 | review | First posts | |||
| Nov 22, 2014 at 17:01 | |||||
| Nov 22, 2014 at 16:10 | history | asked | Hossein Ebadi | CC BY-SA 3.0 |