A new numerical method for a class of Volterra and Fredholm integral equations

In the present work, we introduce a new numerical method based on a strong version of the mean-value theorem for integrals to solve quadratic Volterra integral equations and Fredholm integral equations of the second kind, for which there are theoretical monotonic non-negative solutions. By means of an equality theorem, the integral that appears in the aforementioned equations is transformed into one that enables a more accurate numerical solution with fewer calculations than other previously described methods. Convergence analysis is given.