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.

With the continuous development of society, the pressure of human beings is increasing, and the problem of psychological counseling for school students is getting more and more serious, which has brought great challenges to the education and management of school students. Universities should cultivate students’ professional ability on knowledge and practical skills; we should pay more attention to their psychological counseling and develop and design a simple and efficient learning environment. It is very necessary to establish a psychological evaluation system for college students. This article is based on the design and application of the mobile education information system for psychological education. It highlights that the current psychological counseling problems in school education are indispensable. To better manage the psychological counseling problems faced by many students, 67% of the students have many psychological problems, and the mental health of students in school education and psychological counseling have become the common concern and urgent problems of all college managers. This paper uses the methods of literature research, behavior interview, and experimental investigation to investigate the complementary relationship between the connotation of education and psychological counseling from the data of the fuzzy integral model of psychological counseling, so as to pay more attention to the students’ mental health problems and make the students grow up healthily. The experimental results of this article show that there is still a lot of room for improvement in the use of mobile education information systems to improve their ability to carry out psychological counseling work.

The comprehensive application and development of multimedia technology and network technology in education is a research hotspot for a long time now and for a long time. Mechanical design is an important technical basic course for mechanical and related majors in colleges and universities. It is practical and comprehensive. This paper takes mechanical design teaching as the starting point, designs and develops a multimedia network education platform that meets the mechanical design teaching of colleges and universities. The platform fully utilizes the comprehensive advantages of streaming media technology, WebRTC technology and Web mining technology to enable teachers and students to attend classes and communicate remotely online. Through the comparative experiments on the classes of Chengnan College, the results show that with the platform teaching, the students' motivation for learning in the mechanical design discipline is enhanced, the learning investment is increased, and the teachers are satisfied with the classroom atmosphere and teaching effects. This shows that the platform can improve the teaching effect.

With the rapid development of Internet technology in China, mechanical drawing plays a more and more important role in social development and practice. The main purpose is to use the course of mechanical drawing to accurately represent the appearance, size, principle and technology of the machine. It is often called the language of communication in the industry. In order to make mechanical drawing better applied and practiced, and to make maximum use of Internet technical resources, the establishment of multimedia courseware teaching mechanism is the development trend of mechanical drawing.In order to adapt to the trend of network information, based on the multimedia environment, this paper studies the application of animation technology in mechanical drawing teaching, and constructs a small multimedia teaching platform. Through the explanation of animation courseware, students can better understand the making and principle of mechanical drawing, and cultivate students' divergent thinking. The teaching platform combines teaching material knowledge with practice to deepen students' understanding of the basic content of mechanical drawing. Finally, the rationality and practicability of the system are analyzed by investigating the platform users. The results show that the application of animation technology in mechanical drawing teaching is reasonable and practical.

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