global error estimation of linear multistep methods through the rungekutta methods

In this paper, we study the global truncation error of the linear multistep methods (lmm) in terms of local truncation error of the corresponding rungekutta schemes. the key idea is the representation of lmm with a corresponding rungekutta method. for this, we need to consider the multiple step of a linear multistep method as a single step in the corresponding rungekutta method. therefore, the global error estimation of a lmm through the rungekutta method will be provided. in this estimation, we do not take into account the effects of roundoff errors. the numerical illustrations show the accuracy and efficiency of the given estimation.