Abstract
A particular case of the Hermite interpolation method, namely the two-point Taylor formula, is utilized to construct a numerical technique for solving Fredholm integral equations (FIEs) of the second kind. This method can be applied to approximate the solution of both linear and nonlinear FIEs, and systems of nonlinear FIEs. The sufficient conditions to guarantee the convergence of the proposed method are provided through our analytical studies. Also, the error estimation is presented for this method. Furthermore, the efficiency of the method is confirmed by applying it to solve several illustrative examples. Numerical experiments confirm that the method is easy to implement and gives accurate approximations in acceptable computational times.
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