edith@ai.toronto.edu (Edith Fraser) (02/12/90)
Department of Computer Science, University of Toronto (GB = Gailbraith Building, 35 St. George Street) ------------------------------------------------------------- NUMERICAL ANALYSIS SEMINAR GB244, at 3:00 p.m., Friday 23 February 1990 Professor J.H. Verner Queen's University "On the Derivation of High Order Interpolants" It is now accepted that interpolatory formulas for Runge-Kutta formula pairs provide useful complementary information to that provided by the traditional approximations at discrete points. The author has developed unified strategies for deriving various types of explicit methods. These strategies have been extended for the construction of appended interpolatory formulas. These extensions utilize a matrix representation of the order information of the basic pair of methods which arises from the conventional order conditions for methods. This formulation will be motivated and explained. A lower bound on the number of stages required for interpolants of orders p>5 will be discussed. Finally, some curious relations among the interpolatory coefficients obtained will be displayed for discussion.