TY - JOUR
TI - A Neural Network Technique for the Derivation of Runge-Kutta Pairs
Adjusted for Scalar Autonomous Problems
AU - Kovalnogov, Vladislav N.
AU - Fedorov, V, Ruslan
AU - Khakhalev, Yuri A.
AU - and Simos, Theodore E.
AU - Tsitouras, Charalampos
JO - Interdisciplinary Applied Mathematics
PY - 2021
VL - 9
TODO - 16
SP - null
PB - MDPI
SN - null
TODO - 10.3390/math9161842
TODO - initial value problem; scalar autonomous; Runge-Kutta; differential
evolution; functionally fitted methods
TODO - 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.
ER -