Numerical solution of time-varing functional differential equations via Haar Wavelets

Haar wavelets, the simplest form of wavelet, were introduced by Alfred Haar. Haar wavelets are an orthogonal subset of Hilbert space. Haar wavelet is one of the most practical methods for solving time-varing functional differential equation due to the characteristics of orthogonal and symmetry. In addition, due to the use of the basic function of the Haar, the number of computational operations is reduced. In this study, firstly, the characteristics of the Haar wavelet introduced, then integrals operational matrices and Haar base coefficients are constructed, and using the matrices, the time-varing functional differential equation is approximated. The results of this method are presented in two examples. An error analysis of the proposed method is also provided. We implemented this method on several examples and numerical results were presented in the table of error values. The desirable accuracy of the results is observed for the number of points in the examples given

Keywords:

Haar Wavelet , Time-varing functional differential equations , Operational matrix , Haar bases.