A boundary-value problem for linear PDAEs

Wiesław Marszałek; Zdzisław Trzaska

International Journal of Applied Mathematics and Computer Science (2002)

  • Volume: 12, Issue: 4, page 487-491
  • ISSN: 1641-876X

Abstract

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We analyze a boundary-value problem for linear partial differential algebraic equations, or PDAEs, by using the method of the separation of variables. The analysis is based on the Kronecker-Weierstrass form of the matrix pencil[A,-λ_n B]. A new theorem is proved and two illustrative examples are given.

How to cite

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Marszałek, Wiesław, and Trzaska, Zdzisław. "A boundary-value problem for linear PDAEs." International Journal of Applied Mathematics and Computer Science 12.4 (2002): 487-491. <http://eudml.org/doc/207604>.

@article{Marszałek2002,
abstract = {We analyze a boundary-value problem for linear partial differential algebraic equations, or PDAEs, by using the method of the separation of variables. The analysis is based on the Kronecker-Weierstrass form of the matrix pencil[A,-λ\_n B]. A new theorem is proved and two illustrative examples are given.},
author = {Marszałek, Wiesław, Trzaska, Zdzisław},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {linear multivariable systems; boundary-value problems; differential algebraic equations; linear partial differential algebraic equations; separation of variables; Kronecker-Weierstrass form; matrix pencil},
language = {eng},
number = {4},
pages = {487-491},
title = {A boundary-value problem for linear PDAEs},
url = {http://eudml.org/doc/207604},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Marszałek, Wiesław
AU - Trzaska, Zdzisław
TI - A boundary-value problem for linear PDAEs
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 4
SP - 487
EP - 491
AB - We analyze a boundary-value problem for linear partial differential algebraic equations, or PDAEs, by using the method of the separation of variables. The analysis is based on the Kronecker-Weierstrass form of the matrix pencil[A,-λ_n B]. A new theorem is proved and two illustrative examples are given.
LA - eng
KW - linear multivariable systems; boundary-value problems; differential algebraic equations; linear partial differential algebraic equations; separation of variables; Kronecker-Weierstrass form; matrix pencil
UR - http://eudml.org/doc/207604
ER -

References

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  1. Brenan K.E., Campbell S.L. and Petzold L.R. (1996): Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. - Philadelphia, PA: SIAM. Zbl0844.65058
  2. Campbell S.L. (1982): Singular Systems of Differential Equations II. - Marshfield, MA: Pitman. Zbl0482.34008
  3. Campbell S.L. and Marszałek W. (1999): Index of infinite dimensional differential algebraic equations. - Math. Comp. Model. Dynam. Syst., Vol. 5, No. 1, pp. 18-42. Zbl0922.35040
  4. Campbell S.L. and Marszałek W. (1996): ODEDAE integrators and MOL problems. -Zeitschrift fur Angewandte Mathematik und Mechanik (ZAMM), pp. 251-254. Zbl0900.65274
  5. Campbell S.L. and Marszałek W. (1998): Mixed symbolic-numerical computations with general DAEs: An applications case study. - Numer. Alg., Vol. 19, No. 1, pp. 85-94. Zbl0929.34003
  6. Campbell S.L. and Marszałek W. (1997): DAEs arising from traveling wave solutions of PDEs I. - J. Comp. Appl. Math., Vol. 82, No. 1-2, pp. 41-58. Zbl0952.34002
  7. Clark K.D. and Petzold L.R. (1989): Numerical solution of boundary value problem in differential algebraic systems. - SIAM J. Sci. Stat. Comp., Vol. 10, No. 5, pp. 915-936. Zbl0677.65089
  8. Griepentrog E. and Marz R. (1986): Differential-Algebraic Equations and Their Numerical Treatment. - Treubner-Texte zur Mathematik, Band 88, Treubner: Leipzig. Zbl0629.65080
  9. Haberman R. (1998): Elementary Applied Partial Differential Equations(with Fourier Series and Boundary Value Problems). - Upper Saddle River, NJ: Prentice Hall. Zbl0949.35001
  10. Lewis F.L. (1986): A survey of linear singular systems. - Circ.Syst. Signal Process., Vol. 5, No. 1, pp. 3-36. Zbl0613.93029
  11. Marszałek W. and Trzaska Z.W. (1995): Analysis of implicit hyperbolic multivariable systems. - Appl. Math. Model., Vol. 19, No. 7, pp. 400-410. Zbl0832.65105
  12. Marszałek W. and Campbell S.L. (1999): DAEs arising from traveling wave solutions of PDEs II. - Comp. Math. Appl., Vol. 37, No. 1, pp. 15-34. Zbl0952.34003
  13. Pipilis K.G. (1990): Higher Order Moving Finite Element Methods for Systems Described by Partial Differential-Algebraic Equations. - Ph.D. Thesis, Dept. Chem. Eng., Imperial College, London. 
  14. Strauss W.A. (1992): Partial Differential Equations: An Introduction. - New York: Wiley. Zbl0817.35001
  15. Trzaska Z.W. and Marszałek W. (1993): Singular distributed parameter systems. - IEE Proc., Pt.D. Contr. Th. Appl., Vol. 140, No. 5, pp. 305-308. Zbl0786.93054
  16. Watkins D.S. (1991): Fundamentals of Matrix Computations.- New York: Wiley. Zbl0746.65022

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