Numerical Solution of Locally Loaded Volterra Integral Equations

Loaded Volterra integral equations represent a novel class of integral equations that have attracted considerable attention in recent years due to their numerous applications in various fields of science and engineering. This class of Volterra integral equations is characterized by the presence of a loading function, which complicates their theoretical and numerical analysis. In this paper, we study Volterra equations with locally loaded integral operators. The existence and uniqueness of their solutions are examined. A collocation-type method for the approximate solution of such equations is proposed, based on piecewise linear approximation of the exact solution. To confirm the convergence of the method, several numerical results for solving model problems are provided.