Exponentially Accurate Rayleigh–Ritz Method for Fractional Variational Problems

Abstract

A high accurate Rayleigh–Ritz method is developed for solving fractional variational problems (FVPs). The Jacobi polyfractonomials proposed by Zayernouri and Karniadakis (2013, “Fractional Sturm–Liouville EigenProblems: Theory and Numerical Approximation,â€‌ J. Comput. Phys., 252(1), pp. 495–517.) are chosen as basis functions to approximate the true solutions, and the Rayleigh–Ritz technique is used to reduce FVPs to a system of algebraic equations. This method leads to exponential decay of the errors, which is superior to the existing methods in the literature. The fractional variational errors are discussed. Numerical examples are given to illustrate the exponential convergence of the method.