Numerical solution of a nonuniquely solvable Volterra integral equation using extrapolation methods

In this work the numerical solution of a Volterra integral equation with a certain weakly singular kernel, depending on a real parameter μ, is considered. Although for certain values of μ this equation possesses an infinite set of solutions, we have been able to prove that Eulerʹs method converges to a particular solution. It is also shown that the error allows an asymptotic expansion in fractional powers of the stepsize, so that general extrapolation algorithms, like the E-algorithm, can be applied to improve the numerical results. This is illustrated by means of some examples.