High-order finite difference schemes for the solution of second-order BVPs

Authors:
Pierluigi Amodio;Ivonne Sgura
Affiliations:
Dipartimento di Matematica, Universití degli Studi di Bari, Via Orabona 4, 70125 Bari, Italy;Dipartimento di Matematica, Universití degli Studi di Lecce, 73100 Lecce, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

We introduce new methods in the class of boundary value methods (BVMs) to solve boundary value problems (BVPs) for a second-order ODE. These formulae correspond to the high-order generalizations of classical finite difference schemes for the first and second derivatives. In this research, we carry out the analysis of the conditioning and of the time-reversal symmetry of the discrete solution for a linear convection-diffusion ODE problem. We present numerical examples emphasizing the good convergence behavior of the new schemes. Finally, we show how these methods can be applied in several space dimensions on a uniform mesh.