An optimized linearization-based predictor-corrector algorithm for the numerical simulation of nonlinear FDEs

This study presents an optimized algorithm of the predictor-corrector approaches for the numerical simulation of initial value problems consisting of nonlinear fractional differential equations. The proposed optimized algorithm implements a linear approximation of the nonlinear problem to improve the efficiency of the predictor-corrector methods. The mathematical derivation of the proposed algorithm is introduced. Some illustrative examples are examined to demonstrate the validity and accuracy of the presented algorithm. The obtained numerical results confirm that the suggested optimized linearization-based predictor-corrector algorithm displays better performance and accuracy than the existing methods. The suggested algorithm is expected to be further implemented to get numerical approximations of many nonlinear Caputo-type fractional differential equations.