Convergence and Stability Analysis of Runge-Kutta Type Methods for Volterra Integral Equations of the Second Kind

摘要

Runge-Kutta type methods for Volterra integral equations of the second kind are studied which contain additional terms in order to extend the stability region. The order of convergence is derived and for kernel functions of the form K(x,y,f) = (A+Bx+Cy)f the stability behavior of the methods is considered by deriving the characteristic equation of the difference equation satisfied by the numerical solution. For a number of Runge-Kutta methods stability regions are given and the stabilizing effect of the additional terms is illustrated.