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.W e 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.
High Order Finite Difference Schemes for the Solution of Second Order BVPs
SGURA, Ivonne
2005-01-01
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.W e 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.File in questo prodotto:
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