Geodesic
Two-stage complex Rosenbrock schemes for stiff systems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 2, pp. 270-287 Cet article a éte moissonné depuis la source Math-Net.Ru

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New two-stage Rosenbrock schemes with complex coefficients are proposed for stiff systems of differential equations. The schemes are fourth-order accurate and satisfy enhanced stability requirements. A one-parameter family of $L1$-stable schemes with coefficients explicitly calculated by formulas involving only fractions and radicals is constructed. A single $L2$-stable scheme is found in this family. The coefficients of the fourth-order accurate $L4$-stable scheme previously obtained by P. D. Shirkov are refined. Several fourth-order schemes are constructed that are high-order accurate for linear problems and possess the limiting order of $L$-decay. The schemes proposed are proved to converge. A symbolic computation algorithm is developed that constructs order conditions for multistage Rosenbrock schemes with complex coefficients. This algorithm is used to design the schemes proposed and to obtain fifth-order accurate conditions. 
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A. B. Alshin; E. A. Alshina; A. G. Limonov. Two-stage complex Rosenbrock schemes for stiff systems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 2, pp. 270-287. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_2_a5/

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