On existence and numerical solution of a new class of nonlinear second degree integro-differential Volterra equations with a convolution kernel

This paper considers a new class of nonlinear second degree integro-differential Volterra equations with a convolution kernel. We derive some sufficient conditions to establish the existence and uniqueness of solutions by using the Schauder fixed point theorem. Moreover, the Nyström method is applied to obtain an approximate solution of the proposed Volterra equation. Numerical examples are given to validate the adduced results.