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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:176

Article

Amodio, P ; Sgura, I

关键词: finite difference schemes;    boundary value methods;    two-point boundary value problems;    conditioning analysis;   

DOI  :  10.1016/j.cam.2004.07.008

来源: Elsevier

【 摘 要 】

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. (C) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

Free