%0 Journal Article
%A Eslahchi, M.R.
%A Abedzadeh, A.
%T Extended Jacobi and Laguerre Functions and their Applications
%J Iranian Journal of Mathematical Sciences and Informatics
%V 13
%N 2
%U http://ijmsi.ir/article-1-916-en.html
%R
%D 2018
%K Sturm-Liouville theory, Orthogonal polynomials, Ordinary dierential equations, Non-classical Sturm-Liouville problems, Spectral method, Collocation method, Galerkin.,
%X 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.
%> http://ijmsi.ir/article-1-916-en.pdf
%P 143-161
%& 143
%!
%9 Research paper
%L A-10-611-1
%+
%G eng
%@ 1735-4463
%[ 2018