Constructing Two-Dimensional Multi-Wavelet for Solving Two-Dimensional Fredholm Integral Equations
Mohsen Rabbani · Journal of Operational Research In Its Applications ( Applied Mathematics ) - Lahijan Azad University · 2011
In this paper, a two-dimensional multi-wavelet is constructed in terms of Chebyshev polynomials. The constructed multi-wavelet is an orthonormal basis for 22 [0,1] L space. By discretizing two-dimensional Fredholm integral equation reduce to a algebraic system. The obtained system is solved by the Galerkin method in the subspace of 22 [0,1] L by using twodimensional multi-wavelet bases. Because the bases of subspaces are orthonormal, so the above mentioned system has a small dimension and also high accuracy in approximating solution of integral equations. For one-dimensional case, a similar works are done in [4, 5], which they have small dimension and high accuracy. In this article, we extend one-dimensional case to twodimensional by extending and by choosing good functions on two axes. Numerical results show that the above mentioned method has a good accuracy.