  In research problems that involve the use of numerical methods for solving
systems of ordinary differential equations (ODEs), it is often required to
select the most efficient method for a particular problem. To solve a Cauchy
problem for a system of ODEs, Runge-Kutta methods (explicit or implicit ones,
with or without step-size control, etc.) are employed. In that case, it is
required to search through many implementations of the numerical method and
select coefficients or other parameters of its numerical scheme. This paper
proposes a library and scripts for automated generation of routine functions in
the Julia programming language for a set of numerical schemes of Runge-Kutta
methods. For symbolic manipulations, we use a template substitution tool. The
proposed approach to automated generation of program code allows us to use a
single template for editing, instead of modifying each individual function to
be compared. On the one hand, this provides universality in the implementation
of a numerical scheme and, on the other hand, makes it possible to minimize the
number of errors in the process of modifying the compared implementations of
the numerical method. We consider Runge-Kutta methods without step-size
control, embedded methods with step-size control, and Rosenbrock methods with
step-size control. The program codes for the numerical schemes, which are
generated automatically using the proposed library, are tested by numerical
solution of several well-known problems.
