Collocation and iterated collocation methods for a class of weakly singular Volterra integral equations

Authors:
Teresa Diogo
Affiliations:
Centro de Matemática e Aplicaçíes, Instituto Superior Técnico/UTL, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

We discuss the convergence properties of spline collocation and iterated collocation methods for a weakly singular Volterra integral equation associated with certain heat conduction problems. This work completes the previous studies of numerical methods for this type of equations with noncompact kernel. In particular, a global convergence result is obtained and it is shown that discrete superconvergence can be achieved with the iterated collocation if the exact solution belongs to some appropriate spaces. Some numerical examples illustrate the theoretical results.