Geodesic
About one new two-stages Rosenbrock scheme for differential-algebraic systems
Matematičeskoe modelirovanie, Tome 23 (2011) no. 3, pp. 139-160.

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The equations for coefficients of two-stages Rosenbrock scheme guarantying approximation with third order of accuracy for differential-algebraic system (index 1) are obtained in this paper. These coefficients are complex numbers. New 2-stages Rosenbrock scheme is constructed. It is L2-stable. This scheme has accuracy $O(\tau^3)$ for differential-algebraic systems and $O(\tau^4)$ for pure differential stiff systems. Convergence of this scheme is proved. This scheme was tested on several standard stiff tests and compared with previously know scheme of the same class.
Keywords: stiff-system, differential-algebraic systems, Rosenbrock schemes, schemes with complex parameters, A-stability, L-stability. 
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A. B. Alshin; E. A. Alshina. About one new two-stages Rosenbrock scheme for differential-algebraic systems. Matematičeskoe modelirovanie, Tome 23 (2011) no. 3, pp. 139-160. http://geodesic.mathdoc.fr/item/MM_2011_23_3_a11/

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