Name
Title | ||
|---|---|---|
Fractional spectral and pseudo-spectral methods in unbounded domains: Theory and applications. |
Abstract | ||
|---|---|---|
This paper is intended to provide exponentially accurate Galerkin, Petrov–Galerkin and pseudo-spectral methods for fractional differential equations on a semi-infinite interval. We start our discussion by introducing two new non-classical Lagrange basis functions: NLBFs-1 and NLBFs-2 which are based on the two new families of the associated Laguerre polynomials: GALFs-1 and GALFs-2 obtained recently by the authors in [28]. With respect to the NLBFs-1 and NLBFs-2, two new non-classical interpolants based on the associated- Laguerre–Gauss and Laguerre–Gauss–Radau points are introduced and then fractional (pseudo-spectral) differentiation (and integration) matrices are derived. Convergence and stability of the new interpolants are proved in detail. Several numerical examples are considered to demonstrate the validity and applicability of the basis functions to approximate fractional derivatives (and integrals) of some functions. Moreover, the pseudo-spectral, Galerkin and Petrov–Galerkin methods are successfully applied to solve some physical ordinary differential equations of either fractional orders or integer ones. Some useful comments from the numerical point of view on Galerkin and Petrov–Galerkin methods are listed at the end. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.jcp.2017.02.060 | Journal of Computational Physics |
Keywords | Field | DocType |
Fractional calculus,Associated Laguerre polynomials,Generalized associated Laguerre functions of the first- and second-kind,Non-classical Lagrange basis functions,Fractional differentiation and integration matrices,Convergence,Stability,Spectral methods,Pseudo-spectral methods,Galerkin and Petrov–Galerkin methods,Fractional Basset force equation,Lane–Emden equation,Fractional relaxation–oscillation equation,Fractional ordinary differential equations,Jacobi polyfractonomials,Generalized Jacobi functions,Preconditioner matrix | Differential equation,Mathematical optimization,Ordinary differential equation,Laguerre polynomials,Matrix (mathematics),Mathematical analysis,Galerkin method,Fractional calculus,Basis function,Spectral method,Mathematics | Journal |
Volume | ISSN | Citations |
338 | 0021-9991 | 7 |
PageRank | References | Authors |
0.46 | 15 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hassan Khosravian-Arab | 1 | 11 | 1.36 |
| Mehdi Dehghan | 2 | 3022 | 324.48 |
| M. R. Eslahchi | 3 | 88 | 13.65 |