A novel and eective method based on Haar wavelets and Block Pulse Functions(BPFs) is proposed to solve nonlinear Fredholm integro-dierential equations of fractional order.The operational matrix of Haar wavelets via BPFs is derived and together with Haar waveletoperational matrix of fractional integration are used to transform the mentioned equation to asystem of algebraic equations. Our new met...

In this paper, we present a method for calculated the numerical approximation of nonlinear Fredholm Volterra Hammerstein integral equation, which uses the properties of rationalized Haar wavelets. The main tool for error analysis is the Banach fixed point theorem. An upper bound for the error was obtained and the order of convergence is analyzed. An algorithm is presented to compute and illustr...

a novel and eective method based on haar wavelets and block pulse functions(bpfs) is proposed to solve nonlinear fredholm integro-dierential equations of fractional order.the operational matrix of haar wavelets via bpfs is derived and together with haar waveletoperational matrix of fractional integration are used to transform the mentioned equation to asystem of algebraic equations. our new m...

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...

This paper describes a new data structure called the \Haar Spectral Diagram" (or HSD) useful for representing the Haar spectrum of boolean functions. An alternative ordering of Haar coe cients is used to represent the Haar transform matrix in terms of a Kronecker product yielding a natural decision-diagram based representation. The resulting graph is a pointdecomposition of the Haar spectrum us...

Haar transform is known to have the smallest computational requirement and has been used mainly for pattern recognition and image processing. Although the properties of Haar spectra of Boolean functions have considerable interest and attraction, the majority of publications to date have employed the Walsh rather than Haar transform in their considerations. It is mainly due to the fact that up t...

The Weyl criterion is shown in the terms of Price functions and Haar type functions. We define the so-called modified integrals of Price and Haar type functions and obtain the analogues of the criterion of Weyl, the inequalities of LeVeque and Erdös-Turan and the formula of Koksma in the terms of the modified integrals of Price and Haar type functions.

We give a new generalization for Haar functions. The generalization starts from the Walsh-like functions and based on the connection between the original Walsh and Haar systems. We generalize the Haar– Fourier Transform too.