Geodesic
Rosenbrock schemes with complex coefficients for stiff and differential algebraic systems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 8, pp. 1392-1414 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Rosenbrock schemes with complex coefficients for stiff and differential algebraic systems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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A. B. Alshin; E. A. Alshina; N. N. Kalitkin; A. B. Koryagina. Rosenbrock schemes with complex coefficients for stiff and differential algebraic systems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 8, pp. 1392-1414. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_8_a4/

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