ON A REGULARIZATION OF INDEX 2 DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH PROPERLY STATED LEADING TERM

doi:10.1016/S0252-9602(11)60239-7

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (2): 383-398.doi: 10.1016/S0252-9602(11)60239-7

ON A REGULARIZATION OF INDEX 2 DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH PROPERLY STATED LEADING TERM

刘红¹|宋永忠^2*

1.Teaching Group of Mathematics, Zhenjiang Watercraft College of PLA, Zhenjiang 212003, China|2.School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, China

收稿日期:2007-09-19 修回日期:2010-03-28 出版日期:2011-03-20 发布日期:2011-03-20
通讯作者: 宋永忠 E-mail:hongliu001@sina.com; yzsong@njnu.edu.cn
基金资助:
Project supported by the Foundation for the Authors of the National Excellent Doctoral Thesis Award of China (200720)

ON A REGULARIZATION OF INDEX 2 DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH PROPERLY STATED LEADING TERM

LIU Hong¹, SONG Yong-Zhong^2*

1.Teaching Group of Mathematics, Zhenjiang Watercraft College of PLA, Zhenjiang 212003, China|2.School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, China

Received:2007-09-19 Revised:2010-03-28 Online:2011-03-20 Published:2011-03-20
Contact: SONG Yong-Zhong E-mail:hongliu001@sina.com; yzsong@njnu.edu.cn
Supported by:
Project supported by the Foundation for the Authors of the National Excellent Doctoral Thesis Award of China (200720)

摘要/Abstract

摘要：

In this article, linear regular index 2 DAEs A(t)[D(t)x(t)]'+B(t)x(t)=q(t) are considered. Using a decoupling technique, initial condition and boundary condition are properly formulated. Regular index 1DAEs are obtained by a regularization method. We study the behavior of the solution of the regularization system via asymptotic expansions. The error analysis between the solutions of the DAEs and its regularization system is given.

关键词: Differential-algebraic equations (DAEs), properly stated leading term, index, regularization

Abstract:

Key words: Differential-algebraic equations (DAEs), properly stated leading term, index, regularization

中图分类号:

34A09

刘红, 宋永忠. ON A REGULARIZATION OF INDEX 2 DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH PROPERLY STATED LEADING TERM[J]. 数学物理学报(英文版), 2011, 31(2): 383-398.

LIU Hong, SONG Yong-Zhong. ON A REGULARIZATION OF INDEX 2 DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH PROPERLY STATED LEADING TERM[J]. Acta mathematica scientia,Series B, 2011, 31(2): 383-398.

参考文献

[1] Balla K, M\"arz R. A unified approach to linear differential algebraic equations and their adjoint equations. Z Anal Anwend, 2002, 21: 783--802

[2]  Balla K, M\"arz R. Linear boundary value problems for differential algebraic equations. Miskolc Math Notes, 2004, 5: 3--18

[3]  Gear C W, Petzold L R. ODE methods for the solution of differential/algebraic systems. SIAM J Numer Anal, 1984, 21: 716--728

[4]  Hanke H, M\"arz R, Neubauer A. On the regularization of a class of nontransferable differential-algebraic equations. J Differ Equations, 1988, 73: 119--132

[5] Higueras I, März R. Differential algebraic equations with properly stated leading terms. Comput Math Appl, 2004, 48: 215--235

[6] Higueras I, M\"arz R, Tischendorf C. Stability preserving integration of index-1DAEs. Appl Numer Math, 2003, 45: 175--200

[7] Higueras I, M\"arz R, Tischendorf C. Stability preserving integration of index-2 DAEs. Appl Numer Math, 2003, 45: 201--229

[8] Koch O, März R, Praetorius D, Weinm\"{u}ller E. Collocation methods for index 1 DAEs with a singularity of the first kind. Math Comp, 2010, 79(269): 281--304

[9] Lamour R. Index determination and calculation of consistent initial values. Comput Math Appl, 2005, 50: 1125--1140

[10] Lamour R, Mazzia F. Computation of consistent initial values for properly stated index 3 DAEs. BIT Numer Math, 2009, 49: 161--175

[11] März R. The index of linear differential algebraic equations with properly stated leading terms. Result Math, 2002, 42: 308--338

[12] März R. Differential algebraic equations anew. Appl Numer Math, 2002, 42: 315--335

[13] März R. Solvability of linear differential algebraic equations with properly stated leading terms. Result Math, 2004, 45: 88--105

[14] März R. Fine decouplings of regular differential algebraic equations. Result Math, 2004, 46: 57--72

[15] März R. Characterizing differential algebraic equations without the use of derivative arrays. Comput Math Appl, 2005, 50: 1141--1156

[16] März R, Riaza R. Linear differential-algebraic equations with properly stated leading term: regular points. J Math Anal Appl, 2006,
323: 1279--1299

\REF{17} M\"arz R, Riaza R. Linear differential-algebraic equations with properly stated-leading term: A-critical points. Math Comput Model Dyn Syst, 2007, 13: 291--314

[18] März R, Riaza R. Linear differential-algebraic equations with properly stated-leading term: B-critical points. Dyn Syst, 2008, 23: 505--522

[19] O'Malley R E. Singular Perturbation Methods for Ordinary Differential Equations. Applied Mathematical Sciences 89. New York: Springer-Verlag, 1991

[20] Riaza R. Differential-Algebraic Systems: Analytical Aspects and Circuit Applications. World Scientific, 2008

[21] Riaza R, März R. A simpler construction of the matrix chain defining the tractability index of linear DAEs. Appl Math Lett, 2008, 21:
326--331

[22] Schulz S. Four lectures on differential-algebraic equations//Tech Report 497. New Zealand: The University of Auckland, 2003

[23] Soto M S, Tischendorf C. Numerical analysis of DAEs from coupled circuit and semiconductor simulation. Appl Numer Math, 2005, 53: 471--488

[24] Song Y. Solvability of higher index time-varying linear differential-algebraic equations. Acta Mathematica Scientia, 2001, 21(B): 77--92

ON A REGULARIZATION OF INDEX 2 DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH PROPERLY STATED LEADING TERM

ON A REGULARIZATION OF INDEX 2 DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH PROPERLY STATED LEADING TERM

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