Application of the Adams-Bashfort-Mowlton method to the numerical study of linear fractional oscillators models

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 are considered as tools for numerical analysis. An analysis of the errors of the methods is carried out, it is shown that the ABM method is more accurate and converges faster to an exact solution than the ENFDS method.