The aim of this talk is to consider continuous extensions of two-step Runge-Kutta methods (TSRK) for the numerical solution of Ordinary Differential Equations and Volterra Integral Equations through modified collocation techniques, based on algebraic polynomials satisfying opportune interpolation and collocation conditions. In order to derive methods with strong stability properties, we drop some of those conditions, achieving the class of A-stable almost collocation TSRK methods. We describe the constructive techniques, discuss the order of the resulting methods, analyze their stability properties and show some numerical examples on problems of interest in applications.
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