An extrapolation method for a Volterra integral equation with weakly singular kernel
Subject of the study is the Volterra integral equation of the second kind \[ u(t)= \int_0^t K(t,s)p(t,s)u(s)ds+ f(t),\qquad t\in[0,T], \] \[ \text{with }p(t,s):={1\over\sqrt\pi}\frac{1}{\sqrt{[\ln(t/s)]}} \frac{s^{\mu-1}}{t^{\mu-1}} \qquad \text{or}\quad p(t,s):=\frac{s^{\mu-1}}{t^\mu}, \] where \(\mu>0\), \(K(t,s)\) smooth and \(f\) at least differentiable in the theorems. An asymptotic error expansion of Euler's method is developed to affiliate Richardson extrapolation. Some numerical examples.
scientific article; zbMATH DE number 1036649