Exponential fitting Direct Quadrature methods for Volterra integral equations

This paper is the first approach to the solution of Volterra integral equation by exponential fitting methods. We have developed a Direct Quadrature method, which uses a class of ef-based quadrature rules adapted to the current problem to solve. We have analyzed the convergence of the method and have found different formulas for the coefficients, which limit rounding errors for small stepsizes. Numerical experiments for comparison with other DQ methods are presented.