Some Aspects of the Numerical Analysis of a Fractional Duffing Oscillator with a Fractional Variable Order Derivative of the Riemann-Liouville Type

Abstract

In this paper, we consider some aspects of the numerical analysis of the mathematical model of fractional Duffing with a derivative of variable fractional order of the Riemann-Liouville type. Using numerical methods: an explicit finite-difference scheme based on the Grunwald-Letnikov and Adams-Bashford-Moulton approximations (predictor-corrector), the proposed numerical model is found. These methods have been verified with a test case. It is shown that the predictor-corrector method has a faster convergence than the method according to the explicit finite-difference scheme. For these schemes, using Runge's rule, estimates of the computational accuracy were made, which tended to unity with an increase in the number of calculated grid nodes.