Stability Regions in the Numerical Treatment of Volterra Integral Equations

Abstract

“Step-by-step” methods (in which there is the possibility of unstable error propagation) occur in the approximate solution of first and second kind integral equations of Volterra type. We discuss a definition of stability, and its application to determine regions of stability for such methods applied to simple test equations. This gives new insight into the suitability of numerical methods in practice.