Article
| Title: | The eigenvalues of symmetric Sturm-Liouville problem and inverse potential problem, based on special matrix and product formula (English) |
| Author: | Liu, Chein-Shan |
| Author: | Li, Botong |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 69 |
| Issue: | 3 |
| Year: | 2024 |
| Pages: | 355-372 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | The Sturm-Liouville eigenvalue problem is symmetric if the coefficients are even functions and the boundary conditions are symmetric. The eigenfunction is expressed in terms of orthonormal bases, which are constructed in a linear space of trial functions by using the Gram-Schmidt orthonormalization technique. Then an $n$-dimensional matrix eigenvalue problem is derived with a special matrix ${\bf A}:=[a_{ij}]$, that is, $a_{ij}=0$ if $i+\nobreak j$ is odd.\looseness +1 \endgraf Based on the product formula, an integration method with a fictitious time, namely the fictitious time integration method (FTIM), is developed to obtain the higher-index eigenvalues. Also, we recover the symmetric potential function $q(x)$ in the Sturm-Liouville operator by specifying a few lower-index eigenvalues, based on the product formula and the Newton iterative method. (English) |
| Keyword: | symmetric Sturm-Liouville problem |
| Keyword: | inverse potential problem |
| Keyword: | special matrix eigenvalue problem |
| Keyword: | product formula |
| Keyword: | fictitious time integration method |
| MSC: | 34A55 |
| MSC: | 34B24 |
| DOI: | 10.21136/AM.2024.0005-21 |
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| Date available: | 2024-05-17T07:47:48Z |
| Last updated: | 2024-05-20 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152354 |
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