Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
8
10.52547/ijmsi
14
8888
13
en
jalali
1397
7
1
gregorian
2018
10
1
13
2
online
1
fulltext
en
Extended Jacobi and Laguerre Functions and their Applications
عمومى
General
پژوهشي
Research paper
<p dir="RTL"><span dir="LTR"> </span></p>
<p>The aim of this paper is to introduce two new extensions of the Jacobi and Laguerre<br>
polynomials as the eigenfunctions of two non-classical Sturm-Liouville problems. We<br>
prove some important properties of these operators such as: These sets of functions are<br>
orthogonal with respect to a positive de nite inner product de ned over the compact<br>
intervals [-1, 1] and [0,1), respectively and also these sequences form two new orthog-<br>
onal bases for the corresponding Hilbert spaces. Finally, the spectral and Rayleigh-Ritz<br>
methods are carry out using these basis functions to solve some examples. Our nu-<br>
merical results are compared with other existing results to con rm the eciency and<br>
accuracy of our method.</p>
Sturm-Liouville theory, Orthogonal polynomials, Ordinary dierential equations, Non-classical Sturm-Liouville problems, Spectral method, Collocation method, Galerkin.
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http://ijmsi.ir/browse.php?a_code=A-10-611-1&slc_lang=en&sid=1
M.R.
Eslahchi
`10031947532846006522`

10031947532846006522
No
Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University
A.
Abedzadeh
`10031947532846006523`

10031947532846006523
Yes
Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University