The cohesiveness of G-symplectic methods (Q891785)

The author shortly reviews the G-symplectic methods, previously introduced by himself, provides an example of such method, the so-called 4123A method and illustrates the deleterious effect of parasitism. Then he is concerned with the G-symplectic methods with zero parasitic growth and introduces the concept of cohesiveness. This concept has been revealed in order ``to describe the holding together of the multiple values generated as output from one step''. For a G-symplectic method in partitioned diagonal form, the main result shows the slow growth of the deviation from cohesiveness. Eventually, it is numerically confirmed for the above mentioned method.