Two-step diagonally-implicit collocation based methods for Volterra Integral Equations

Authors:
Dajana Conte;Raffaele Dambrosio;Beatrice Paternoster
Affiliations:
Dipartimento di Matematica, Universití di Salerno, Via Ponte Don Melillo, I-84084 Fisciano (SA), Italy;Dipartimento di Matematica, Universití di Salerno, Via Ponte Don Melillo, I-84084 Fisciano (SA), Italy;Dipartimento di Matematica, Universití di Salerno, Via Ponte Don Melillo, I-84084 Fisciano (SA), Italy
Venue:
Applied Numerical Mathematics
Year:
2012

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Abstract

We introduce a family of diagonally-implicit continuous methods for the numerical integration of Volterra Integral Equations. The derived methods are characterized by a lower triangular or diagonal coefficient matrix of the nonlinear system for the computation of the stages which, as it is known, can be exploited to get an efficient implementation. The constructed methods have a high uniform order of convergence together with strong stability properties (e.g. A-stability).