$B$-series for complete $(m,k)$-method

S. A. Konev


Abstract: Symbolic expression for derivatives of numerical solution of the complete $(m,k)$-method are constructed. The expressions are described with Butcher rooted trees. The concept of stages 'color' is actively used in proof of the main theorem. The possible applications of obtained results are discussed.

Keywords: stiff systems, Butcher trees, Rosenbrock methods, $(m,k)$-methods, order conditions.

DOI: 10.20948/prepr-2020-45