We consider a family of explicit Runge–Kutta pairs of orders six and five without any additional property (reduced truncation errors, Hamiltonian preservation, symplecticness, etc.). This family offers five parameters that someone chooses freely. Then, we train them in order for the presented method to furnish the best results on a couple of Kepler orbits, a certain interval and tolerance. Consequently, we observe an efficient performance on a wide range of orbital problems (i.e., Kepler for a variety of eccentricities, perturbed Kepler with various disturbances, Arenstorf and Pleiades). About $1.8$ digits of accuracy is gained on average over conventional pairs, which is truly remarkable for methods coming from the same family and order.

The purpose of this study is to explore the relationship between school belonging and subjective social status of middle school students, and whether mental health plays an intermediary role between them. Taking 484 middle school students as subjects, they completed the school belonging scale, subjective social status scale and general health questionnaire. The results show that: (1) There is a significant positive correlation between school belonging, mental health and subjective social status of middle school students. (2) Middle school students’ sense of school belonging can positively predict their subjective social status, and can also indirectly influence their subjective social status through mental health, which plays an intermediary role between school belonging and subjective social status.