非线性常微分方程初值问题的间断有限元

Abstract

Abstract: In this paper the initial value problem of nonlinear ODE is solved with discontinuous finite elements of order u'=f(x,u),u(0)=u_0. For m≥1, the authors prove that the left limits of discontinuous finite elements of order m at their node have a superconvergence estimate (u-U(x_j-0)=O(h^2m+1) and at characteristic points x_jiof order m+1 of every elements. There is the superconvergence estimate (u-U)(x_ji)=O(h^m+2).

Key words: Nonlinear, Ordinary Differential Equation(ODE), Initial value problem, Discontinuous finite element, Superconvergence

CLC Number:

65N30

Li Tianran;Chen Chuanmiao. Discontinuous Finite Elements in Solving Initial Value Problem of Nonlinear ODE[J].Acta mathematica scientia,Series A, 2006, 26(1): 63-068.

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Discontinuous Finite Elements in Solving Initial Value Problem of Nonlinear ODE

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