High-order finite difference schemes for the solution of second-order BVPs |
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Affiliation: | 1. Dipartimento di Matematica, Università degli Studi di Bari, Via Orabona 4, 70125 Bari, Italy;2. Dipartimento di Matematica, Università degli Studi di Lecce, 73100 Lecce, Italy |
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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. |
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