We present a new family of compactly supported and symmetric biorthogonal wavelet systems. Each refinement mask in this family has tension parameter ω. When ω = 0, it becomes the minimal length biorthogonal Coifman wavelet system [22]. Choosing ω away from zero, we can get better smoothness of the refinable functions at the expense of slightly larger support. Though the construction of the new ...

In this paper, we have proposed a Haar wavelet quasilinearization method to solve the well known Blasius equation. The method is based on the uniform Haar wavelet operational matrix defined over the interval [0, 1]. In this method, we have proposed the transformation for converting the problem on a fixed computational domain. The Blasius equation arises in the various boundary layer problems of...

A multiresolution approach based on a modified wavelet transform called the tree-structured wavelet transform or wavelet packets is proposed. The development of this transform is motivated by the observation that a large class of natural textures can be modeled as quasi-periodic signals whose dominant frequencies are located in the middle frequency channels. With the transform, it is possible t...

The wavelet X-ray transform computes one-dimensional wavelet transforms along lines in Euclidian space in order to perform a directional time-scale analysis of functions in several variables. A fast algorithm is proposed which executes this transformation starting with values given on a cartesian grid that represent the underlying function. The algorithm involves a rotation step and wavelet ana...

The purpose of this study is to develop a new approach in modeling and simulation of a reverse osmosis desalination system by using fractional differential equations. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. Examples are developed to illustrate the fractional differential techniq...

In this article, a novel and efficient collocation method based on Fibonacci wavelets is proposed for the numerical solution of non-linear Hunter–Saxton equation. Firstly, operational matrices integration associated with are constructed by following strategy Chen Hsiao. The merged used to convert given problem into system algebraic equations that can be solved any classical method, such as Newt...

1 This paper is concerned with the implementation of the wavelet Galerkin scheme for the Laplacian in two dimensions. We utilize biorthogonal wavelets constructed by A. Cohen, I. Daubechies and J.-C. Feauveau in 3] for the discretization leading to quasi-sparse system matrices which can be compressed without loss of accuracy. We develop algorithms for the computation of the compressed system ma...