Application of the Adams-Bashfort-Mowlton Method to the Numerical Study of Linear Fractional Oscillators Models

TL;DR

This paper analyzes numerical methods for linear fractional oscillator models, demonstrating that the Adams-Bashfort-Moulton method offers higher accuracy and faster convergence compared to explicit nonlocal finite-difference schemes.

Contribution

It introduces and compares the ABM method with ENFDS for fractional oscillators, highlighting its superior accuracy and convergence properties.

Findings

ABM method is more accurate than ENFDS.

ABM converges faster to the exact solution.

Error analysis supports the effectiveness of ABM.

Abstract

The paper presents a numerical analysis of the class of mathematical models of linear fractional oscillators, which is the Cauchy problem for a differential equation with derivatives of fractional orders in the sense of Gerasimov-Caputo. A method based on an explicit nonlocal finite-difference scheme (ENFDS) and the Adams-Bashfort-Moulton (ABM) method is considered a numerical analysis tool. An analysis of the errors of the methods is carried out, and it is shown that the ABM method is more accurate and converges faster to an exact solution than the ENFDS method.