Abstract
In the present paper we develop a numerical collocation scheme for integral equations based on the interpolation method which uses the so-called neural network operators activated by ramp functions. The proposed collocation scheme allows to solve both linear and nonlinear Volterra integral equations of the second kind; the convergence of the numerical method has been proved under standard assumptions. Numerical examples have been provided and discussed; the proposed method has been compared with the classical piecewice polynomials collocation method and a method based on sigmoidal functions, such as the Heaviside and the logistic functions.
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