Stability of reducible quadrature methods for Volterra integral equations of the second kind
Based on the test equation \[ y(t)=1+\int^{t}_{0}(\lambda +\mu t+\nu s)y(s)ds \] a stability analysis of reducible quadrature methods for second kind Volterra integral equations is presented. Since the above integral equation is equivalent to a second order differential equation (with non-constant coefficients), the numerical solution satisfies a finite recurrence relation. The boundedness of the analytical solution of the differential equation as well as that of the numerical solution of the recurrence relation are investigated. The results are then illustrated for the \(\theta\)-method. The importance of the above test equation is still not clear, since in applications usually the kernel is bounded or converges to zero when t-s\(\to \infty\).
scientific article; zbMATH DE number 3915591
scientific article