Geodesic
Optimum $L$-decremented rosebrock schemes with complex coefficients for stiff ODE
Matematičeskoe modelirovanie, Tome 4 (1992) no. 8, pp. 47-57.

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The extension of coefficients of Rosenbrock type schemes to the complex numbers allows to construct methods with good $L$-decrementation. Therefore such kind of two-stages schemes were investigated theoretically in detail for the case of autonomous system. There were found out several sets of coefficients which lead to the methods of accuracy $O(\tau^4)$ and of highest $L$-decrementation for stability function as well as for internal stability function. 
@article{MM_1992_4_8_a3,
     author = {P. D. Shirkov},
     title = {Optimum $L$-decremented rosebrock schemes with complex coefficients for stiff {ODE}},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {47--57},
     publisher = {mathdoc},
     volume = {4},
     number = {8},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1992_4_8_a3/}
}
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P. D. Shirkov. Optimum $L$-decremented rosebrock schemes with complex coefficients for stiff ODE. Matematičeskoe modelirovanie, Tome 4 (1992) no. 8, pp. 47-57. http://geodesic.mathdoc.fr/item/MM_1992_4_8_a3/