Summary
Based on the theory of Butcher series this paper developes the order conditions for Rosenbrock methods and its extensions to Runge-Kutta methods with exact Jacobian dependent coefficients. As an application a third order modified Rosenbrock method with local error estimate is constructed and tested on some examples.
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Nørsett, S.P., Wolfbrandt, A. Order conditions for Rosenbrock type methods. Numer. Math. 32, 1–15 (1979). https://doi.org/10.1007/BF01397646
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DOI: https://doi.org/10.1007/BF01397646