Numerical methods solving the semi-explicit differential-algebraic equations by implicit multistep fixed stepsize methods
- 67 Downloads
We consider three classes of numerical methods for solving the semi-explicit differential-algebraic equations of index 1 and higher. These methods use implicit multistep fixed stepsize methods and several iterative processes including simple iteration, full, and modified Newton iteration. For these methods we prove convergence theorems and derive error estimates. We consider different ways of choosing initial approximations for these iterative methods and investigate their efficiency in theory and practice.
AMS Mathematics Subject Classification65L06
Key words and Phrasesdifferential-algebraic equations index implicit multistep methods iterative methods convergence results error estimates
Unable to display preview. Download preview PDF.
- 2.Yu.Ye. Boyarintsev, V.A. Danilov, A.A. Loginov, V.F. Chistyakov,Numerical methods of solving singular systems, Nauka, Novosibirsk, 1989.Google Scholar
- 6.V.O. Belash, A.L. Glebov, N.Ya. Mar’yashkin, Ye.E. Ovchinnikov,The solution of differential-algebraic systems for the circuit analysis of large integrated circuits, VTs Akad. Nauk S.S.S.R., Moscow, 1991.Google Scholar
- 10.G.Yu. Kulikov,The numerical solution of the autonomous Cauchy problem with an algebraic relation between the phase variables (non-degenerate case), Vestn. MGU Ser. Mat. Mekh., 3 (1993), pp. 6–10.Google Scholar
- 13.G.Yu. Kulikov,The numerical solution of the Cauchy problem with algebraic constrains on the phase variables (with applications in medical cybernetics), The dissertation of candidate of sciences in mathematics, Computational Center of Russian Academy of Sciences, Moscow, 1994.Google Scholar
- 16.A.A. Samarskiy, A.V. Gulin,Numerical methods, Nauka, Moscow, 1989.Google Scholar