Two-step modified collocation methods with structured coefficient matrices

Authors:
Raffaele Dambrosio;Beatrice Paternoster
Affiliations:
Dipartimento di Matematica, Universitá degli Studi di Salerno, 84084 Fisciano (Sa), Italy;Dipartimento di Matematica, Universitá degli Studi di Salerno, 84084 Fisciano (Sa), Italy
Venue:
Applied Numerical Mathematics
Year:
2012

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Abstract

In the context of the numerical integration of initial value problems based on ordinary differential equations, it is the purpose of this paper to introduce a modification of two-step collocation methods, in order to obtain coefficient matrices with a structured shape, to get an efficient implementation. Our aim is the development of new collocation-based methods having high order of convergence and strong stability properties (e.g. A-stability and L-stability). We present the constructive technique, discuss the order of convergence and the stability properties of the resulting methods and provide some numerical results confirming the theoretical expectations.