MATLAB GUI for computing Bessel functions using continued fractions algorithm
Higher order Bessel functions are prevalent in physics and engineering and there exist different methods to evaluate them quickly and efficiently. Two of these methods are Miller's algorithm and the continued fractions algorithm. Miller's algorithm uses arbitrary starting values and normal...
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| Format: | Article |
| Language: | Portuguese |
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Sociedade Brasileira de Física
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| Series: | Revista Brasileira de Ensino de Física |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172011000100003&lng=en&tlng=en |
| _version_ | 1819263079373864960 |
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| author | E. Hernández K. Commeford M.J. Pérez-Quiles |
| author_facet | E. Hernández K. Commeford M.J. Pérez-Quiles |
| author_sort | E. Hernández |
| collection | DOAJ |
| description | Higher order Bessel functions are prevalent in physics and engineering and there exist different methods to evaluate them quickly and efficiently. Two of these methods are Miller's algorithm and the continued fractions algorithm. Miller's algorithm uses arbitrary starting values and normalization constants to evaluate Bessel functions. The continued fractions algorithm directly computes each value, keeping the error as small as possible. Both methods respect the stability of the Bessel function recurrence relations. Here we outline both methods and explain why the continued fractions algorithm is more efficient. The goal of this paper is both (1) to introduce the continued fractions algorithm to physics and engineering students and (2) to present a MATLAB GUI (Graphic User Interface) where this method has been used for computing the Semi-integer Bessel Functions and their zeros. |
| first_indexed | 2024-12-23T20:07:53Z |
| format | Article |
| id | doaj.art-f508e5b6731146848ae8bad87c93e4ad |
| institution | Directory Open Access Journal |
| issn | 1806-1117 1806-9126 |
| language | Portuguese |
| last_indexed | 2024-12-23T20:07:53Z |
| publisher | Sociedade Brasileira de Física |
| record_format | Article |
| series | Revista Brasileira de Ensino de Física |
| spelling | doaj.art-f508e5b6731146848ae8bad87c93e4ad2022-12-21T17:32:53ZporSociedade Brasileira de FísicaRevista Brasileira de Ensino de Física1806-11171806-912633110.1590/S1806-11172011000100003S1806-11172011000100003MATLAB GUI for computing Bessel functions using continued fractions algorithmE. Hernández0K. Commeford1M.J. Pérez-Quiles2Universidad de Pinar del RíoColorado School of MinesUniversitat Politècnica de ValènciaHigher order Bessel functions are prevalent in physics and engineering and there exist different methods to evaluate them quickly and efficiently. Two of these methods are Miller's algorithm and the continued fractions algorithm. Miller's algorithm uses arbitrary starting values and normalization constants to evaluate Bessel functions. The continued fractions algorithm directly computes each value, keeping the error as small as possible. Both methods respect the stability of the Bessel function recurrence relations. Here we outline both methods and explain why the continued fractions algorithm is more efficient. The goal of this paper is both (1) to introduce the continued fractions algorithm to physics and engineering students and (2) to present a MATLAB GUI (Graphic User Interface) where this method has been used for computing the Semi-integer Bessel Functions and their zeros.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172011000100003&lng=en&tlng=enfunções de besselfrações continuadasgui em matlab |
| spellingShingle | E. Hernández K. Commeford M.J. Pérez-Quiles MATLAB GUI for computing Bessel functions using continued fractions algorithm Revista Brasileira de Ensino de Física funções de bessel frações continuadas gui em matlab |
| title | MATLAB GUI for computing Bessel functions using continued fractions algorithm |
| title_full | MATLAB GUI for computing Bessel functions using continued fractions algorithm |
| title_fullStr | MATLAB GUI for computing Bessel functions using continued fractions algorithm |
| title_full_unstemmed | MATLAB GUI for computing Bessel functions using continued fractions algorithm |
| title_short | MATLAB GUI for computing Bessel functions using continued fractions algorithm |
| title_sort | matlab gui for computing bessel functions using continued fractions algorithm |
| topic | funções de bessel frações continuadas gui em matlab |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172011000100003&lng=en&tlng=en |
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