Constructing Two-Dimensional Multi-Wavelet for Solving Two-Dimensional Fredholm Integral Equations

In this paper, a two-dimensional multi-wavelet is constructed in terms of chebyshevpolynomials. the constructed multi-wavelet is an orthonormal basis for l2[0,1]2 space. bydiscretizing two-dimensional fredholm integral equation reduce to a algebraic system. theobtained system is solved by the galerkin method in the subspace of l2[0,1]2 by using twodimensionalmulti-wavelet bases. because the bases of subspaces are orthonormal, so the abovementioned system has a small dimension and also high accuracy in approximating solution ofintegral equations. for one-dimensional case, a similar works are done in [4, 5], which theyhave small dimension and high accuracy. in this article, we extend one-dimensional case to twodimensionalby extending and by choosing good functions on two axes. numerical results showthat the above mentioned method has a good accuracy.