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

Authors:
Pedro Lima;Teresa Diogo
Affiliations:
Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisbon, Portugal;Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Year:
2002

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Abstract

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 Euler's 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.