zbMATH — the first resource for mathematics

Convergence of numerical methods for systems of neutral functional-differential-algebraic equations. (English) Zbl 0853.65077
The authors extend the results on consistency and convergence for numerical methods for the solution of initial value problems in ordinary differential-algebraic equations by P. Deuflhard, E. Hairer and J. Zugck [Numer. Math. 51, 501-516 (1987; Zbl 0635.65083)] and E. Hairer, C. Lubich and M. Roche [Lect. Notes Math. 1409 (1989; Zbl 0683.65050)] to the class of neutral functional differential-algebraic equations. They only consider problems of index 1.

65L05 Numerical methods for initial value problems
34K40 Neutral functional-differential equations
Full Text: EuDML
[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. · Zbl 0699.65057
[2] S. L. Campbell: Singular Systems of Differential Equations. Pitman, London, 1980. · Zbl 0419.34007
[3] S. L. Campbell: Singular Systems of Differential Equations II. Pitman, London, 1982. · Zbl 0482.34008
[4] J. P. Deuflhard: Recent progress in extrapolation methods for ordinary differential equations. SIAM Rev. 27 (1985), 505-535. · Zbl 0602.65047 · doi:10.1137/1027140
[5] P. Deuflhard, E. Hairer, J, Zugck: One-step and extrapolation methods for differential-algebraic systems. Numer. Math. 51 (1987), 501-516. · Zbl 0635.65083 · doi:10.1007/BF01400352 · eudml:133209
[6] C. W. Gear: The simultaneous numerical solution of differential-algebraic equations. IEEE Trans. Circuit Theory TC-18 (1971), 89-95.
[7] C. W. Gear, L. R. Petzold: ODE methods for the solution of differential/algebraic systems. SIAM J. Numer. Anal. 21 (1984), 716-728. · Zbl 0557.65053 · doi:10.1137/0721048
[8] E. Griepentrog, R. März: Differential-Algebraic Equations and Their Numerical Treatment. Teubner-Verlag, Leipzig, 1986. · Zbl 0629.65080
[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. · Zbl 0683.65050 · doi:10.1007/BFb0093947
[10] Z. Jackiewicz: One-step methods of any order for neutral functional differential equations. SIAM J. Numer. Anal. 21 (1984), 486-511. · Zbl 0562.65056 · doi:10.1137/0721036
[11] Z. Jackiewicz, M. Kwapisz: Convergence of waveform relaxation methods for differential algebraic systems. SIAM J. Numer. Anal., In press. · Zbl 0889.34064 · doi:10.1137/S0036142992233098
[12] T. Jankowski: Existence, uniqueness and approximate solutions of problems with a parameter. Zesz. Nauk. Politech. Gdańsk, Mat. 16 (1993), 3-167. · Zbl 0893.34062
[13] L. R. Petzold: Order results for implicit Runge-Kutta methods applied to differential/algebraic systems. SIAM J. Numer. Anal. 23 (1986), 837-852. · Zbl 0635.65084 · doi:10.1137/0723054
[14] L. Tavernini: One-step methods for the numerical solution of Volterra functional differential equations. SIAM J. Numer. Anal. 8 (1971), 786-795. · Zbl 0231.65070 · doi:10.1137/0708072
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.