Abstract
In this article, we discuss the existence of solution using compact operators for Fredholm integral equations system (F.IES). Also we use Galerkin method in a n-dimensional Hilbert space to solve this problem. To reduce the computational operations, we use orthonormal multi-wavelet bases which are constructed by Chebyshev polynomials. Since Chebyshev multi-wavelet bases functions are orthonormal, they help us decrease the operations used in discretizing the integral equations system to an algebraic equations system. The algebraic system contains sparse matrices and it leads to a numerical solution with a high accuracy. Also we consider error analysis in a Sobolev space. Finally for validity and applicability of the above proposed method we compare our results with homotopy perturbation method and Taylor-series expansion method.
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