A splitting iterative method for solving second kind integral equations in reproducing kernel spaces

Abstract In the present paper, we propose a new iterative method to solve integral equations of the second kind in reproducing kernel Hilbert spaces (RKHS). At first, we make appropriate splitting in second kind integral equations and according to this splitting the iterative method will be constructed; then, bases of RKHS and reproducing kernel spaces properties are used to convert this problem to linear system of equations. We move between reproducing kernel spaces by changing bases in order to achieve more accurate approximate solutions. Classically, in iterative RKHS method, the number of iterations should be the same as the number of points; here, we present a type of iterative RKHS method without this limitation. Convergence of the proposed method is investigated, and the efficiency of the method is demonstrated through various examples.

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