A new predictor-corrector method for the numerical solution of fractional differential equations

Abstract

In this paper, first, a new predictor-corrector method( called the modified predictor- corrector method ) for the fractional differential equations is developed. And the new method can be formally viewed as a modification as the classical predictor-corrector method. Second, it is proved that the numerical accuracy of this new method is superior to that of the classical predictor- corrector method by two numerical examples. The comparison with the corresponding results demonstrates that the modified predictor-corrector method is more accurate than the classical predictor-corrector method when solving fractional differential equations numerically.