A general class of Two-Step Runge-Kutta methods for ordinary differential equations.

摘要

general class of Two-Step Runge-Kutta methods is studied, which depend on stage values at two consecutive steps. These methods are special cases of general linear methods introduced by Butcher and are quite efficient with respect to the number of function evaluations required for a given order. General order conditions are derived using the approach proposed recently by Albrecht, and examples of methods are given up to the order five. These methods can be divided into four classes which are appropriate for the numerical solution of nonstiff or stiff differential equations in sequential or parallel computing environments. A general class of variable stepsize continuous Two-Step Runge-Kutta methods is also investigated. The general convergence and order criteria are derived and examples of methods of order p and stage order q = p are given for