The use of wavelets for the calculation of linear control systems with lumped parameters

In many disciplines, problems appear which can be formulated with the aid of differential or integral equations. In simpler cases, such equations can be solved analytically, but for more complicated cases, numerical procedures are needed. In recent times, the wavelet-based methods have gained great popularity, where different wavelet families such as Daubechies, Coiflet, etc. wavelets are applied. A shortcoming of these wavelets is that they do not have an analytic expression. For this reason, differentiation and integration of these wavelets are very complicated. The paper presents algorithms for the numerical solution of linear integral and differential equations based on spline wavelets on the interval. The algorithms generalize the well-known methods based on Haar wavelets, which are a particular case of spline wavelets. The results presented can be applied for the analysis of linear systems with lumped parameters.