A Pair of Two-Step Sixth Stage Implicit Runge-Kutta Type Methods for First Order Ordinary Differential Equations

We use the multistep collocation technique to derive a pair of two-step block hybrid methods incorporating two off-step interpolation points and one off-step collocation point. The block hybrid methods are then reformulated into a pair of new sixth-stage implicit Runge-Kutta-type methods, which are implemented in solving first-order ordinary differential equations. Apart from establishing the basic convergence of the new methods, the new methods are A-stable. Numerical results indicate that the methods compete favorably with similar existing methods in the literature and should be preferred for these types of problems.