A Haar wavelets method of solving differential equations characterizing the dynamics of a current collection system for an electric locomotive

A Haar wavelets method under certain conditions is proposed so as to numerically integrate a system of differential equations and characterize the dynamics of a current collection system for an electric locomotive. A set of Haar wavelets is employed as the basis of approximation. The operational matrix of integration and the Haar Stretch Matrix (HSM), based upon the beneficial properties of Haar wavelets, are derived to tackle the functional differential equations containing a term with a stretched argument. The unknown Haar coefficient matrix will be obtained in the generalized Lyapunov equation. The local property of Haar wavelets is applied to shorten the calculation in the task. A brief comparison of Haar wavelet with other orthogonal functions is demonstrated as well.