Numeric multistep variable methods for perturbed linear system integration

A new special-purpose method of numerical integration for a perturbed linear system of ordinary differential equations is presented, based on Scheifele’s GG-functions method.The new method converts Scheifele’s method in a multistep scheme that conserves the capability of integrating without truncation errors the unperturbed linear system of ODE’s. The new numerical method presents a good property contrasted with other VSVO multistep methods using GG-functions; it adds a simple algebraic procedure for the computation of the coefficients irrespective of what the order is, obtained through recurrence formulas.Some numerical examples are included showing the good behaviour of the new code when it is applied to the class of problems to which it is addressed.