蔡加祥教授，淮阴师范学院

One can elucidate integrability properties of ODEs by knowing the existence of second integrals. However, little is known about how they are preserved, if at all, under numerical methods. In this talk, I will introduce Tapley’s recent work which shows that in general all Runge-Kutta methods will preserve all affine second integrals but not quadratic second integrals. A number of interesting corollaries are discussed, such as the preservation of certain rational integrals by arbitrary Runge-Kutta methods.