Algebraically stable two-step almost collocation methods for ordinary differential equations

We investigate algebraic stability of the new class of two-step almost collocation methods for ordinary differential equations. These continuous methods are obtained by relaxing some of the interpolation and collocation conditions to achieve uniform order of convergence on the whole interval of integration. We describe the search for algebraically stable methods using the crierion based on Nyquist stability function proposed recently by Hill. This criterion leads to the minimization problem in one variable which was solved using fminsearch routine in MATLAB. Examples of algebraically stable methods in this class obtained in this way are presented