线性微分方程边值问题数值求解的多步差分法
首发时间:2008-04-15
摘要:对线性微分方程边值问题, 文献[1]提出了一种统一的多步差分方法,并得到了达到最 高截断误差阶的差分格式. 本文在其基础上,对不同的微分方程和边界条件进行深一步的讨论,并对一些算例进行数值试验,通过与其他文献中的各种方法的结果进行比较, 验证了其方法的优越性.
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Numerical solutions of linear boundary value problems by multi-step difference methods
Abstract:In paper [1], a unified multi-step finite difference method was presented to solve boundary value problems of linear differential equations numerically. The method has the highest order of truncation error, and can be constructed simply by Taylor expansion. In this paper, the multi-step difference methods are further discussed, and applied to solve several differential equations and boundary conditions with different orders. Some examples are employed to evaluate the performance of the method. The numerical results show that it is superior to some methods presented by other papers.
Keywords: Linear boundary value problem Finite difference method Local truncated errors Numerical solution
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No.2050220839812082****
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