Jacobi-Davidson Method For The Second Order Fractional Eigenvalue Problems

We present a Jacobi-Davidson method for solving the second order fractional eigenvalue problems by using the finite difference formulas of the Caputo fractional derivatives. In order to speed up the convergence of the method, we propose the preconditioned generalized minimal residuals method (PGMRES) to solve the correction equation and analyze the spectral clustering property of the preconditioned matrix. Numerical results show that the Jacobi-Davidson method is efficient for solving the fractional eigenvalue problems. (c) 2020 Elsevier Ltd. All rights reserved.