期刊
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
卷 88, 期 16, 页码 3553-3564出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207160.2011.609592
关键词
N-carrier system; Pade approximation; Neumann boundary condition; energy exchange; difference scheme
资金
- Natural Science Research Foundation of Universities in Anhui [KJ2011B112]
- Natural Science Foundation of P.R. China [10962001]
- Guangxi Natural Science Foundation [2010GXNSFA013115, 2011GXNSFD018006]
- Hunan Key Laboratory for Computation and Simulation in Science and Engineering
In this paper, a numerical method is developed to solve an N-carrier system with Neumann boundary conditions. First, we apply the compact finite difference scheme of fourth order for discretizing spatial derivatives at the interior points. Then, we develop a new combined compact finite difference scheme for the boundary, which also has fourth-order accuracy. Lastly, by using a Pade approximation method for the resulting linear system of ordinary differential equations, a new compact finite difference scheme is obtained. The present scheme has second-order accuracy in time direction and fourth-order accuracy in space direction. It is shown that the scheme is unconditionally stable. The present scheme is tested by two numerical examples, which show that the convergence rate with respect to the spatial variable from the new scheme is higher and the solution is much more accurate when compared with those obtained by using other previous methods.
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