New predictor-corrector scheme for solving nonlinear differential equations with Caputo-Fabrizio operator

Abstract

In this paper, we develop a new, simple, and accurate scheme to obtain approximate solution for nonlinear differential equation in the sense of Caputo-Fabrizio operator. To derive this new predictor-corrector scheme, which suits on Caputo-Fabrizio operator, firstly, we obtain the corresponding initial value problem for the differential equation in the Caputo-Fabrizio sense. Hence, by fractional Euler method and fractional trapeziodal rule, we obtain the predictor formula as well as corrector formula. Error analysis for this new method is derived. To test the validity and simplicity of this method, some illustrative examples for nonlinear differential equations are solved.