Geodesic
Development and testing for methods of solving stiff ordinary differential equations
Matematičeskoe modelirovanie i čislennye metody (2014), pp. 95-119

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The paper is aimed at research of the (m,k)-method, CROS, finite superelement method and 4-stage explicit Runge–Kutta method for solving stiff systems of ordinary differential equations. Analysis of tests results showed that the best choice for systems with high stiffness is CROS. The finite superelement method is the «precise» method for solving linear systems of ordinary differential equations, the best supporting method for its implementation is (4,2)-method. The variation of the finite superelement method has been built and tested for solving nonlinear problems, this method proved to be unsuitable for problems with high stiffness.
Keywords: The paper is aimed at research of the (m,k)-method, cros, finite superelement method and 4-stage explicit runge–kutta method for solving stiff systems of ordinary differential equations. analysis of tests results showed that the best choice for systems with high stiffness is cros. the finite superelement method is the «precise» method for solving linear systems of ordinary differential equations, the best supporting method for its implementation is (4,2)-method. the variation of the finite superelement method has been built and tested for solving nonlinear problems, this method proved to be unsuitable for problems with high stiffness. 
@article{MMCM_2014_a6,
     author = {M. P. Galanin and S. R. Khodzhaeva},
     title = {Development and testing for methods of solving stiff ordinary differential equations},
     journal = {Matemati\v{c}eskoe modelirovanie i \v{c}islennye metody},
     pages = {95--119},
     publisher = {mathdoc},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMCM_2014_a6/}
}
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M. P. Galanin; S. R. Khodzhaeva. Development and testing for methods of solving stiff ordinary differential equations. Matematičeskoe modelirovanie i čislennye metody (2014), pp. 95-119. http://geodesic.mathdoc.fr/item/MMCM_2014_a6/