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\begin{document}
\title{Abstract}
\maketitle
In this paper we present a new kind of functions -- the wavelet
integrals and use them as basis functions in an adaptation of the
{\sc Ritz-Galerkin} technique for numerical solution of
differential equations.Studying their properties we come to the
conclusion that they are a promising numerical tool.One of their
advantages is that they are smoother than the standard {\sc
Daubechies} wavelets and in the same time they inherit the
multiresolution properties of these wavelets.Their application
leads to a band matrix.\\ The definition of wavelet integrals on
the interval [0,1] is given following the construction of
orthogonal wavelets on the same interval. To illustrate the above
technique a {\sc Dirichlet} problem on the interval [0,1] is
considered. Several recurrent methods for finding the elements of
this matrix are introduced.Finally an estimation of the
approximation error of the exact solution of the boundary problem
with functions from the space of approximation $\Delta_n$ is made.
\end{document}