Convergence of continuous approximations for discontinuous ODEs

被引：6

作者：

Schiller, H. ^{[1
]}

Arnold, M. ^{[1
]}

机构：

[1] Univ Halle Wittenberg, Inst Math, D-06120 Halle, Germany

来源：

APPLIED NUMERICAL MATHEMATICS | 2012年 / 62卷 / 10期

关键词：

Discontinuous ODE; Regularisation; Filippov solution; Differential inclusion; Multibody system; Coulomb friction; Continuous approximation; SCHEME;

D O I：

10.1016/j.apnum.2012.06.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate a regularisation technique for the solution of discontinuous ordinary differential equations. It is shown that the solutions obtained by the regularisation procedure converge uniformly to an appropriately defined analytical solution whenever the regularisation parameter epsilon goes to zero. Under reasonable conditions the convergence can be shown to be linear in epsilon. Moreover, we present numerical evidence that suggests that the conditions for linear convergence can be further relaxed. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：1503 / 1514

页数：12

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