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- Title
Efficient spectral collocation method for fractional differential equation with Caputo-Hadamard derivative.
- Authors
Zhao, Tinggang; Li, Changpin; Li, Dongxia
- Abstract
Hadamard type fractional calculus involves logarithmic function of an arbitrary exponent as its convolutional kernel, which causes challenge in numerical treatment. In this paper we present a spectral collocation method with mapped Jacobi log orthogonal functions (MJLOFs) as basis functions and obtain an efficient algorithm to solve Hadamard type fractional differential equations. We develop basic approximation theory for the MJLOFs and derive a recurrence relation to evaluate the collocation differentiation matrix for implementing the spectral collocation algorithm. We demonstrate the effectiveness of the new method for the nonlinear initial and boundary problems, i.e, the fractional Helmholtz equation, and the fractional Burgers equation.
- Subjects
FRACTIONAL differential equations; COLLOCATION methods; JACOBI method; ORTHOGONAL functions; APPROXIMATION theory; FRACTIONAL calculus; BURGERS' equation; SPECTRAL theory
- Publication
Fractional Calculus & Applied Analysis, 2023, Vol 26, Issue 6, p2903
- ISSN
1311-0454
- Publication type
Article
- DOI
10.1007/s13540-023-00216-6