The present study investigates the Haar-Sinc collocation method for the solution of the hyperbolic partial telegraph equations. The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices. This technique is used to convert the problem to the solution of linea...

We propose a new “Haar-Fisz” technique for estimating the time-varying, piecewise constant local variance of a locally stationary Gaussian time series. We apply our technique to the estimation of the spectral structure in the Locally Stationary Wavelet model. Our method combines Haar wavelets and the variance stabilizing Fisz transform. The resulting estimator is mean-square consistent, rapidly...

In this paper, we present a framework to determine Haar solutions of Bratu-type equations that are widely applicable in fuel ignition of the combustion theory and heat transfer. The method is proposed by applying Haar series for the highest derivatives and integrate the series. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm. The results show that...

The multiresolution time-domain (MRTD) algorithm is applied to the problem of general two-dimensional electromagnetic scattering. A Haar wavelet expansion is utilized. A parallel between Haar MRTD and the classic Yee finite difference time-domain (FDTD) algorithm is discussed, and results of simulations on canonical targets are shown for comparison. We focus on the incident-field implementation...