A tenth order A-stable two-step hybrid block method for solving initial value problems of ODEs

In this article, a new two-step hybrid block method for the numerical integration of ordinary differential initial value systems is presented. The method is obtained after considering two intermediate points and the approximation of the true solution by an adequate polynomial and imposing collocation conditions. The proposed method has the tenth algebraic order of convergence and is A-stable. The numerical experiments considered revealed the superiority of the new method for solving this kind of problems, in comparison with methods of similar characteristics appeared in the literature.