Least-squares collocation for linear higher-index differential-algebraic equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:317

Article

Hanke, Michael¹  Maerz, Roswitha²  Tischendorf, Caren²  Weinmueller, Ewa³  Wurm, Stefan³ 

[1] KTH Royal Inst Technol, Sch Engn Sci, Dept Math, S-10044 Stockholm, Sweden

[2] Humboldt Univ, Inst Math, D-10099 Berlin, Germany

[3] Vienna Univ Technol, Inst Anal & Sci Comp, A-1040 Vienna, Austria

关键词: Differential-algebraic equation;    Higher index;    Essentially ill-posed problem;    Collocation;    Boundary value problem;    Initial value problem;   

DOI  :  10.1016/j.cam.2016.12.017

来源: Elsevier

【 摘 要 】

Differential-algebraic equations with higher index give rise to essentially ill-posed problems. Therefore, their numerical approximation requires special care. In the present paper, we state the notion of ill-posedness for linear differential -algebraic equations more precisely. Based on this property, we construct a regularization procedure using a least squares collocation approach by discretizing the pre-image space. Numerical experiments show that the resulting method has excellent convergence properties and is not much more computationally expensive than standard collocation methods used in the numerical solution of ordinary differential equations or index-1 differential-algebraic equations. Convergence is shown for a limited class of linear higher-index differential-algebraic equations. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free