Exponentially accurate spectral and spectral element methods for fractional ODEs

• Published in: Journal of computational physics Vol. 257; pp. 460 - 480
• Main Authors: Zayernouri, Mohsen, Karniadakis, George Em
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.01.2014
• Subjects: Asymptotic properties; Basis functions; Dirichlet problem; Discontinuous spectral element method; Distributed memory; Eigenfunctions; Exponential convergence; Jacobi polyfractonomials; Mathematical analysis; Mathematical models; Petrov–Galerkin spectral methods; Spectral methods; Texts; Exponential convergence; Jacobi polyfractonomials; Petrov–Galerkin spectral methods; Discontinuous spectral element method

Current discretizations of fractional differential equations lead to numerical solutions of low order of accuracy. Here, we present different methods for fractional ODEs that lead to exponentially fast decay of the error. First, we develop a Petrov–Galerkin (PG) spectral method for Fractional Initia...