@article{3030447,
    title = "A Neural Network Technique for the Derivation of Runge-Kutta Pairs
Adjusted for Scalar Autonomous Problems",
    author = "Kovalnogov, Vladislav N. and Fedorov, V, Ruslan and Khakhalev, Yuri A. and and Simos, Theodore E. and Tsitouras, Charalampos",
    journal = "Interdisciplinary Applied Mathematics",
    year = "2021",
    volume = "9",
    number = "16",
    publisher = "MDPI",
    doi = "10.3390/math9161842",
    keywords = "initial value problem; scalar autonomous; Runge-Kutta; differential
evolution; functionally fitted methods",
    abstract = "We consider the scalar autonomous initial value problem as solved by an
explicit Runge-Kutta pair of orders 6 and 5. We focus on an efficient
family of such pairs, which were studied extensively in previous
decades. This family comes with 5 coefficients that one is able to
select arbitrarily. We set, as a fitness function, a certain measure,
which is evaluated after running the pair in a couple of relevant
problems. Thus, we may adjust the coefficients of the pair, minimizing
this fitness function using the differential evolution technique. We
conclude with a method (i.e. a Runge-Kutta pair) which outperforms other
pairs of the same two orders in a variety of scalar autonomous problems."
}