TY - JOUR
JF - IJMSI
JO - IJMSI
VL - 13
IS - 2
PY - 2018
Y1 - 2018/10/01
TI - Extended Jacobi and Laguerre Functions and their Applications
TT -
N2 - 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.
SP - 143
EP - 161
AU - Eslahchi, M.R.
AU - Abedzadeh, A.
AD - Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University
KW - Sturm-Liouville theory
KW - Orthogonal polynomials
KW - Ordinary dierential equations
KW - Non-classical Sturm-Liouville problems
KW - Spectral method
KW - Collocation method
KW - Galerkin.
UR - http://ijmsi.ir/article-1-916-en.html
ER -