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Rosenbrock schemes with complex coefficients for stiff and differential algebraic systems

A. B. Alshin^a, E. A. Alshina^a, N. N. Kalitkin^b, A. B. Koryagina<sup>c

a</sup> Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
^b Institute of Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia
^c Moscow State Institute of Electronic Engineering, Technical University, Zelenograd, Moscow, 103498, Russia

Abstract: Many applied problems are described by differential algebraic systems. Complex Rosenbrock schemes are proposed for the numerical integration of differential algebraic systems by the $\varepsilon$-embedding method. The method is proved to converge quadratically. The scheme is shown to be applicable even to superstiff systems. The method makes it possible to perform computations with a guaranteed accuracy. An equation is derived that describes the leading term of the error in the method as a function of time. An algorithm extending the method to systems of differential equations for complex-valued functions is proposed. Examples of numerical computations are given.

Key words: systems of stiff differential algebraic equations, Rosenbrock scheme with complex coefficients.

UDC: 519.622.2

Received: 24.03.2006

 English version: Computational Mathematics and Mathematical Physics, 2006, 46:8, 1320–1340

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