Stability analysis of ef Gaussian direct quadrature methods for Volterra integral equations

The present paper analyzes the numerical stability of exponentially fitted Gaussian direct quadrature methods for Volterra integral equations. By applying the exponential fitting technique, the coefficients of these methods are specially tuned on the problem. The analysis of numerical stability of these methods with respect to the classical basic test equation is carried out, which takes into account the dependence of the methods both on the stepsize and on the problem parameters. Several stability regions are shown and some numerical experiments confirm theoretical expectations.