In this paper, we develop an accurate and efficient Haar wavelet solution of Fisher's equation , a prototypical reaction–diffusion equation. The solutions of Fisher's equation are characterized by propagating fronts that can be very steep for large values of the reaction rate coefficient. There is an ongoing effort to better adapt Haar wavelet methods to the solution of differential equations w...

Wavelets are mathematical tools for hierarchically decomposing functions. Wavelet Transform has been proved to be a very useful tool for image processing in recent years. It allows a function which may be described in terms of a coarse overall shape, plus details that range from broad to narrow. The most distinctive feature of Haar Transform lies in the fact that it lends itself easily to simpl...

This study presents a novel approach for simulating the spread of Omicron variant SARS-CoV-2 virus using fractional-order COVID-19 models and Haar wavelet collocation method. The proposed model considers various factors that affect transmission, while method provides an efficient accurate solution fractional derivatives used in model. analyzes impact valuable insights into its transmission dyna...

in this paper, an effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (rbfs). we present an algorithm based on interpolation by radial basis functions including multiquadratics (mqs), using legendre-gauss-lobatto nodes and weights. also a theorem is proved for convergence of the algorithm. some numerical examples are presented...

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...

Contents Preface ix 1. Wavelet and frame transforms originated from continuous and discrete splines, Amir Z. Averbuch and Valery A. Zheludev 1 1.1. Introduction 1 1.2. Preliminaries 4 1.3. Prediction filters originated from splines 9 1.4. Biorthogonal wavelet transforms generated by filter banks with downsampling factor N = 2 (diadic transforms) 17 1.5. Application of spline-based wavelet trans...

In this paper, we present a numerical scheme using uniform Haar wavelet approximation and quasilinearization process for solving some nonlinear oscillator equations. In our proposed work, quasilinearization technique is first applied through Haar wavelets to convert a nonlinear differential equation into a set of linear algebraic equations. Finally, to demonstrate the validity of the proposed m...

This paper analytically formulates both the optimal quantization noise allocation ratio and the coding gain of the two-dimensional morphological Haar wavelet transform. The two-dimensional morphological Haar wavelet transform has been proposed as a nonlinear wavelet transform. It has been anticipated for application to nonlinear transform coding. To utilize a transformation to transform coding,...

A wavelet method to the solution for time-fractional partial differential equation, by which combining with Haar wavelet and operational matrix to discretize the given functions efficaciously. The time-fractional partial differential equation is transformed into matrix equation. Then they can be solved in the computer oriented methods. The numerical example shows that the method is effective.