@article{He2024, 
author = {Yu He and Jianing Yang and Theodore E. Simos and Charalampos Tsitouras},
title = {A novel class of Runge-Kutta-Nyström pairs sharing orders 8(6)},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {2},
pages = {4882-4895},
keywords = {initial Value Problem, second order, Runge-Kutta-Nyström},
url = {https://www.sciopen.com/article/10.3934/math.2024237},
doi = {10.3934/math.2024237},
abstract = {We are examining a second-order system of non-stiff Initial Value Problems (IVP), focusing on a scenario where the first derivatives are not present. In the realm of solving IVPs, Runge-Kutta-Nyström (RKN) pairs have proven to be highly effective. In order to achieve a pair with eighth and sixth order accuracy, we need to find a solution to a well-defined set of equations regarding the coefficients. Traditionally, pairs are constructed to go through eight stages per step. However, we propose a novel approach with nine stages per step, which enables the creation of pairs with orders    8 and    6 that have notably smaller truncation errors. Our paper introduces a new pair that, as expected, outperforms existing pairs of the same orders in a range of important problems.}
}