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Article

Zubik-Kowal, Barbara
Propagation of errors in dynamic iterative schemes. (English). In: Mikula, Karol (ed.): Proceedings of Equadiff 14. Conference on Differential Equations and Their Applications, Bratislava, July 24-28, 2017. Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, Bratislava, 2017. pp. 97-106
MSC: 65L04, 65L20, 65L70
Keywords:
Dynamic iterations, waveform relaxation, Gauss-Seidel schemes, convergence, error bounds
Summary:
We consider iterative schemes applied to systems of linear ordinary differential equations and investigate their convergence in terms of magnitudes of the coefficients given in the systems. We address the question of whether the reordering of equations in a given system improves the convergence of an iterative scheme.
References:
[1] Butcher, J. C.: Numerical Methods for Ordinary Differential Equations. Second edition, John Wiley & Sons, Ltd., Chichester, 2008. MR 2401398
[2] Burrage, K.: Parallel and Sequential Methods for Ordinary Differential Equations. Oxford University Press, Oxford, 1995. MR 1367504
[3] Miekkala, U., Nevanlinna, O.: Convergence of dynamic iteration methods for initial value problems. SIAM J. Sci. Stat. Comput. 8 (1987), pp. 459–482. DOI 10.1137/0908046 | MR 0892300
[4] Miekkala, U., Nevanlinna, O.: Iterative solution of systems of linear differential equations. Acta Numerica (1996), pp. 259–307. DOI 10.1017/S096249290000266X | MR 1624607
[5] Zubik-Kowal, B.: Improving the convergence of iterative schemes. in preparation.
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