Numerical Methods for the Minimum Energy Among Three Dynamic Systems Governed by a Class of Weakly Singular Integro-Differential Equations

In this study, we presented numerical methods for determining the minimum energy state among three dynamic systems governed by a class of integro-differential equation with weakly singular kernels (Abel-type). These equations were developed from a class of integro-differential equations originating from an aeroelasticity problem. By weighting energy criteria for the three systems, we intend to numerically reveal the most stable energy state for the systems with various initial conditions and tracking targets. A part of the numerical scheme is constructed by interchanging the differentiation and integration operations in the integro-differential equation. Promising numerical results are provided.