Spectral deferred correction method for fractional initial value problem with Caputo-Hadamard derivative

This paper considers an efficient and accurate spectral deferred correction (SDC) method for the initial value problem (IVP) with Caputo-Hadamard derivative. We first apply the basic idea of the SDC method to derive the numerical scheme. Then the iteration matrix which is the key to convergence of the proposed scheme can be obtained for the linear problem. Detailed computation of history term is presented using the spectral collocation method based on mapped Jacobi log orthogonal functions (MJLOFs). Finally, numerical simulations for both linear and nonlinear cases are shown to verify the feasibility and efficiency of the proposed method.