Construction and implementation of two-step continuous methods for Volterra integral equations

It is the purpose of this paper to construct an error estimation for highly stable two-step continuous methods derived in [7], in order to use it in a variable stepsize implementation. New families of two step almost collocation methods are constructed, by using a collocation technique which permits to increase the uniform order of one step collocation methods, without increasing the computational cost and by maintaining good stability properties, thus avoiding the order reduction phenomenon. Numerical experiments confirm the effectiveness of the proposed methods.