Document Type
Article
Publication Date
9-15-2016
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
This paper introduces two families of orthogonal polynomials on the interval (−1,1), with weight function w(x)=1. The first family satisfies the boundary condition p(1)=0, and the second one satisfies the boundary conditions p(-1)=p(1)=0. These boundary conditions arise naturally from PDEs defined on a disk with Dirichlet boundary conditions and the requirement of regularity in Cartesian coordinates. The families of orthogonal polynomials are obtained by orthogonalizing short linear combinations of Legendre polynomials that satisfy the same boundary conditions. Then, the three-term recurrence relations are derived. Finally, it is shown that from these recurrence relations, one can efficiently compute the corresponding recurrences for generalized Jacobi polynomials that satisfy the same boundary conditions.
Publication Title
SpringerPlus
Volume
5
First Page
1
Last Page
29
Recommended Citation
Richardson, M.,
Lambers, J. V.
(2016). Recurrence Relations for Orthogonal Polynomials for PDEs In Polar and Cylindrical Geometrics. SpringerPlus, 5, 1-29.
Available at: https://aquila.usm.edu/fac_pubs/16745
Comments
This is a post-peer-review, pre-copyedit version of an article published in 'SpringerPlus'. The final authenticated version is available online at: 10.1186/s40064-016-3217-y. The following terms of use apply: https://www.springer.com/gp/open-access/publication-policies/aam-terms-of-use.