Title of article :
Extended Jacobi and Laguerre Functions and Their Applications
Author/Authors :
Abedzadeh, Azam Department of Applied Mathematics - Faculty of Mathematical Sciences - Tarbiat Modares University - Tehran, Iran , Eslahchi, MR Department of Applied Mathematics - Faculty of Mathematical Sciences - Tarbiat Modares University - Tehran, Iran
Abstract :
The aim of this paper is to introduce two new extensions of
the Jacobi and Laguerre polynomials as the eigenfunctions of two nonclassical Sturm-Liouville problems. We prove some important properties of these operators such as: These sets of functions are orthogonal with respect to a positive denite inner product dened over the compact intervals [1; 1] and [0;1), respectively and also these sequences form two new orthogonal 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 numerical results are compared with other existing results to conrm the eciency and accuracy of our method
Keywords :
Rayleigh-Ritz method , Sturm-Liouville theory , Orthogonal polynomials , Ordinary differential equations , Non-classical Sturm-Liouville problems , Galerkin method , Collocation method , Spectral method
Journal title :
Astroparticle Physics
