An improved PC scheme for nonlinear fractional differential equations: Error and stability analysis

A novel computationally effective fractional predictor-corrector (PC) scheme is proposed to solve fractional differential equations involving Caputo derivative. The properties of the Caputo derivative are used to reduce the fractional differential equation into a Volterra integral equation. To design high order numerical solution of FDEs, the Simpson's 3/8 rule is applied to the Volterra type integral equation. The scheme is capable of handling both linear and nonlinear fractional differential equations. A detailed error analysis and stability analysis of the numerical scheme are rigorously established. The proposed scheme is compared with the PC schemes of literature for illustrating the effectiveness of the algorithm.