Fractional spectral and pseudo-spectral methods in unbounded domains: Theory and applications
| Autor: | Mohammad Reza Eslahchi, Mehdi Dehghan, Hassan Khosravian-Arab |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Numerical Analysis
Physics and Astronomy (miscellaneous) Applied Mathematics Mathematical analysis Basis function 010103 numerical & computational mathematics 01 natural sciences Mathematics::Numerical Analysis Computer Science Applications Fractional calculus 010101 applied mathematics Computational Mathematics Integer Modeling and Simulation Ordinary differential equation Laguerre polynomials 0101 mathematics Lane–Emden equation Galerkin method Spectral method Mathematics |
| Zdroj: | Journal of Computational Physics. 338:527-566 |
| ISSN: | 0021-9991 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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