The numerical stability of multistep methods for convolution Volterra integral equations Nonsingular equations

AbstractA family of test equations is suggested for first and second kind nonsingular Volterra integral equations with convolution kernels. It is shown that the numerical stability of multistep methods when applied to these test equations can be characterised as the requirement that the roots of polynomials lie inside or on the unit circle. Stability results are presented for a sample of methods including some stability regions in graphical form