Improved spectral deferred correction methods for fractional differential equations

Abstract

In this study, we improved the spectral deferred correction method for nonlinear fractional differential equations. First, problems were transformed into equivalent nonlinear Volterra integral equations with weakly singular kernels. We then employed the fractional Adams–Bashforth method in the prediction step and used the Gauss quadrature formula and fractional Adams–Moulton scheme in the correction step. Moreover, a vigorous error analysis for the numerical scheme was conducted. Finally, computational results for some experiments were reported to demonstrate the accuracy and ease of implementation of the improved numerical scheme.