Accelerazione della convergenza per metodi di risoluzione di equazioni differenziali ordinarie

In this paper a procedure for the acceleration of the convergence is given. It allows the doubling of the order of the multistep methods for the numerical solution of the ordinary differential equation $$y' = f(x,y),y_0 = y(x_0 );{}_{x_0 }^x \in a,b].$$ This acceleration is applicable to any method of orderp≥1 whatsoever, and it requires the evaluation of the globalp-th derivate of the functionf(x, y). Special attention is confined to the 2⁰ and 3⁰ order methods, and a numerical exemple is provided.