Volume 13, Issue 2 (10-2018)
IJMSI 2018, 13(2): 143-161 |
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Eslahchi M, Abedzadeh A. Extended Jacobi and Laguerre Functions and their Applications. IJMSI 2018; 13 (2) :143-161
URL: http://ijmsi.ir/article-1-916-en.html
URL: http://ijmsi.ir/article-1-916-en.html
Abstract:
The aim of this paper is to introduce two new extensions of the Jacobi and Laguerre
polynomials as the eigenfunctions of two non-classical Sturm-Liouville problems. We
prove some important properties of these operators such as: These sets of functions are
orthogonal with respect to a positive de nite inner product de ned over the compact
intervals [-1, 1] and [0,1), respectively and also these sequences form two new orthog-
onal bases for the corresponding Hilbert spaces. Finally, the spectral and Rayleigh-Ritz
methods are carry out using these basis functions to solve some examples. Our nu-
merical results are compared with other existing results to con rm the eciency and
accuracy of our method.
Keywords: Sturm-Liouville theory, Orthogonal polynomials, Ordinary dierential equations, Non-classical Sturm-Liouville problems, Spectral method, Collocation method, Galerkin.
Type of Study: Research paper |
Subject:
General
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