In this paper we construct a flatlet biorthogonal multiwavelets System. Then, we use this system for numerical solution of Integro-differential equations. The good properties of this system, i.e., biorthogonality and more vanishing moments lead to efficient and accurate solutions. Some test problems with known solutions are presented and the numerical results are given to show the efficiency of...

A suucient condition for the orthonormality of reenable vector functions is given. Then we construct examples of orthonormal compactly supported multiscal-ing functions and their associated multiwavelets with arbitrarily high regularity in the univariate and bivariate settings. We use this suucient condition to check their orthonor-mality.

A procedure of the extension of orthogonal multiresolution analysis is introduced by assuming that φ1(x) ia an orthogonal uniscaling function and constructing a new orthogonal multiscaling function Φ(x) = [φ1(x), φ2(x)]. Moreover, an explicit formula of the orthogonal multiwavelets associated with Φ(x) is obtained. Finally, a construction example is given. 2000 Mathematics Subject Classificatio...

K e y w o r d s W a v e l e t s , Multiwavelets, Approximation order, Refinement equations, Subdivision. 1. I N T R O D U C T I O N Wavele t t heo ry is based on the idea of mul t i r eso lu t ion analys is (MRA) . Usually, an M R A is gene r a t e d by one scal ing funct ion. However, such wavelets canno t possess t he p rope r t i e s of shor t s u p p o r t , s y m m e t r y or an t i symmet...

Given a pair of biorthogonal, compactly supported multiwavelets, we present an algorithm for raising their approximation orders to any desired level, using one lifting step and one dual lifting step. Free parameters in the algorithm are explicitly identified, and can be used to optimize the result with respect to other criteria.