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G. Yu. Kulikov

One–step methods and implicit extrapolation technique for index 1 differential–algebraic systems

In this paper we first formulate and prove a number of theorems concerning the convergence of combined numerical one-step methods for index 1 differential-algebraic systems. Then, we use these results to justify an implicit extrapolation technique and show their practical importance. Second, we give a theory of adjoint and symmetric one-step methods for differential-algebraic equations and we also determine symmetric methods among Runge–Kutta formulae. We prove that algebraically stable symmetric Runge–Kutta formulae are symplectic and they have a structure which is in some sense similar to the structure of Gauss methods. Finally, we come to the concept of quadratic extrapolation for index 1 differential-algebraic systems and develop an advanced version of the localglobal step size control based on the extrapolation technique. Numerical tests support the theoretical results of the paper.

Russian Journal of Numerical Analysis and Mathematical Modelling, Walter de Gruyter

Print ISSN: 0927-6467
Volume: 19, 12/2004
Pages: 527 - 553

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