On solving systems of differential algebraic equations

Marian Kwapisz

Applications of Mathematics (1992)

  • Volume: 37, Issue: 4, page 257-264
  • ISSN: 0862-7940

Abstract

top
In the paper the comparison method is used to prove the convergence of the Picard iterations, the Seidel iterations, as well as some modifications of these methods applied to approximate solution of systems of differential algebraic equations. The both linear and nonlinear comparison equations are emloyed.

How to cite

top

Kwapisz, Marian. "On solving systems of differential algebraic equations." Applications of Mathematics 37.4 (1992): 257-264. <http://eudml.org/doc/15714>.

@article{Kwapisz1992,
abstract = {In the paper the comparison method is used to prove the convergence of the Picard iterations, the Seidel iterations, as well as some modifications of these methods applied to approximate solution of systems of differential algebraic equations. The both linear and nonlinear comparison equations are emloyed.},
author = {Kwapisz, Marian},
journal = {Applications of Mathematics},
keywords = {Picard method; Seidel method; system of differential algebraic equations; convergence; successive approximations; differential algebraic equations; comparison method; Picard iterations; Picard method; Seidel method; system of differential algebraic equations; convergence; successive approximations},
language = {eng},
number = {4},
pages = {257-264},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On solving systems of differential algebraic equations},
url = {http://eudml.org/doc/15714},
volume = {37},
year = {1992},
}

TY - JOUR
AU - Kwapisz, Marian
TI - On solving systems of differential algebraic equations
JO - Applications of Mathematics
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 4
SP - 257
EP - 264
AB - In the paper the comparison method is used to prove the convergence of the Picard iterations, the Seidel iterations, as well as some modifications of these methods applied to approximate solution of systems of differential algebraic equations. The both linear and nonlinear comparison equations are emloyed.
LA - eng
KW - Picard method; Seidel method; system of differential algebraic equations; convergence; successive approximations; differential algebraic equations; comparison method; Picard iterations; Picard method; Seidel method; system of differential algebraic equations; convergence; successive approximations
UR - http://eudml.org/doc/15714
ER -

References

top
  1. E. Bohl, Monotonie: Lösbarkeit und Numerik bei Operatoren-gleichungen, Springer Verlag, Berlin, 1974. (1974) MR0636414
  2. I. Bremer K.R. Schneider, A remark on solving large systems of equations in function spaces, Aplikace Matematiky 35(1990), 494-498. (1990) MR1089930
  3. L. Kantorovich, 10.1007/BF02547750, Acta Math. 71 (1939), 63-97. (1939) MR0000095DOI10.1007/BF02547750
  4. M. Kwapisz, 10.4064/ap-19-1-47-60, Ann. Polon. Math. 19 (1967), 47-60. (1967) Zbl0149.36403MR0210314DOI10.4064/ap-19-1-47-60
  5. M. Kwapisz, 10.4064/ap-22-1-73-87, Ann. Polon. Math. 22(1969), 73-87. (1969) Zbl0184.37802MR0258274DOI10.4064/ap-22-1-73-87
  6. M. Kwapisz, A comparison theorem on the existence and uniqueness of the solution of an integral-functional equation, VII Internationale Konferenz über nichtlineare Schwingungen, Band 1,1, Abhandlungen der AdW, Akademie-Verlag, Berlin, 1977, pp. 481-487. (1977) Zbl0368.45009MR0513188
  7. M. Kwapisz, Some remarks on abstract form of iterative methods in functional equation theory, Commentationes Mathematicae 24 (1984), 281-294. (1984) Zbl0579.47064MR0766465
  8. M. Kwapisz, Some remarks on nonlinear A-contractions, Analele Sţiintifice Ale Universitătii "Al. I. Cuza" - Iasi, 32, s. I a, Mathematică 2 (1986), 17-22. (1986) Zbl0652.47037MR0893678
  9. J. M. Ortega W. C. Rheinboldt, Iterative solutions of nonlinear equations in several variables, Academic Press, New York, 1970. (1970) MR0273810
  10. T. Wazewski, Sur un precédé de prouver la convergence des approximations successives sans utilisation des séries de comparison, Bull. Acad. Sci., sér. sci. math. astr. et phys. 8, 1 (1960), 45-52. (1960) MR0126109

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.