Convergence of numerical methods for systems of neutral functional-differential-algebraic equations
Applications of Mathematics, Tome 40 (1995) no. 6, pp. 457-472

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

DOI MR   Zbl

A general class of numerical methods for solving initial value problems for neutral functional-differential-algebraic systems is considered. Necessary and sufficient conditions under which these methods are consistent with the problem are established. The order of consistency is discussed. A convergence theorem for a general class of methods is proved.
A general class of numerical methods for solving initial value problems for neutral functional-differential-algebraic systems is considered. Necessary and sufficient conditions under which these methods are consistent with the problem are established. The order of consistency is discussed. A convergence theorem for a general class of methods is proved.
DOI : 10.21136/AM.1995.134307
Classification : 34K40, 65L05
Keywords: neutral functional-differential-algebraic systems; consistency; convergence
Jankowski, Tadeusz; Kwapisz, Marian. Convergence of numerical methods for systems of neutral functional-differential-algebraic equations. Applications of Mathematics, Tome 40 (1995) no. 6, pp. 457-472. doi: 10.21136/AM.1995.134307
@article{10_21136_AM_1995_134307,
     author = {Jankowski, Tadeusz and Kwapisz, Marian},
     title = {Convergence of numerical methods for systems of neutral functional-differential-algebraic equations},
     journal = {Applications of Mathematics},
     pages = {457--472},
     year = {1995},
     volume = {40},
     number = {6},
     doi = {10.21136/AM.1995.134307},
     mrnumber = {1353973},
     zbl = {0853.65077},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1995.134307/}
}
TY  - JOUR
AU  - Jankowski, Tadeusz
AU  - Kwapisz, Marian
TI  - Convergence of numerical methods for systems of neutral functional-differential-algebraic equations
JO  - Applications of Mathematics
PY  - 1995
SP  - 457
EP  - 472
VL  - 40
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1995.134307/
DO  - 10.21136/AM.1995.134307
LA  - en
ID  - 10_21136_AM_1995_134307
ER  - 
%0 Journal Article
%A Jankowski, Tadeusz
%A Kwapisz, Marian
%T Convergence of numerical methods for systems of neutral functional-differential-algebraic equations
%J Applications of Mathematics
%D 1995
%P 457-472
%V 40
%N 6
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1995.134307/
%R 10.21136/AM.1995.134307
%G en
%F 10_21136_AM_1995_134307

[1] K. E. Brenan, S. L. Campbell, L. R. Petzold: Numerical Solution of Initial-Value Problems in Differential-Algebraic-Equations. North-Holand, New York, Amsterdam, London, 1989. | MR

[2] S. L. Campbell: Singular Systems of Differential Equations. Pitman, London, 1980. | Zbl

[3] S. L. Campbell: Singular Systems of Differential Equations II. Pitman, London, 1982. | Zbl

[4] J. P. Deuflhard: Recent progress in extrapolation methods for ordinary differential equations. SIAM Rev. 27 (1985), 505–535. | DOI | MR | Zbl

[5] P. Deuflhard, E. Hairer, J, Zugck: One-step and extrapolation methods for differential-algebraic systems. Numer. Math. 51 (1987), 501–516. | DOI | MR

[6] C. W. Gear: The simultaneous numerical solution of differential-algebraic equations. IEEE Trans. Circuit Theory TC-18 (1971), 89–95. | DOI

[7] C. W. Gear, L. R. Petzold: ODE methods for the solution of differential/algebraic systems. SIAM J. Numer. Anal. 21 (1984), 716–728. | DOI | MR

[8] E. Griepentrog, R. März: Differential-Algebraic Equations and Their Numerical Treatment. Teubner-Verlag, Leipzig, 1986. | MR

[9] E. Hairer, Ch. Lubich, M. Roche: The numerical solution of differential-algebraic systems by Runge-Kutta methods. Lecture Notes in Mathematics Nr.  1409, Springer-Verlag, Berlin, Heidelberg, New York, 1989. | MR

[10] Z. Jackiewicz: One-step methods of any order for neutral functional differential equations. SIAM J. Numer. Anal. 21 (1984), 486–511. | DOI | MR | Zbl

[11] Z. Jackiewicz, M. Kwapisz: Convergence of waveform relaxation methods for differential algebraic systems. SIAM J. Numer. Anal., In press. | MR

[12] T. Jankowski: Existence, uniqueness and approximate solutions of problems with a parameter. Zesz. Nauk. Politech. Gdańsk, Mat. 16 (1993), 3–167. | Zbl

[13] L. R. Petzold: Order results for implicit Runge-Kutta methods applied to differential/algebraic systems. SIAM J. Numer. Anal. 23 (1986), 837–852. | DOI | MR | Zbl

[14] L. Tavernini: One-step methods for the numerical solution of Volterra functional differential equations. SIAM J. Numer. Anal. 8 (1971), 786–795. | DOI | MR | Zbl

Cité par Sources :