This work consist of a family of one step rational integrators of order 2k-1 developed for the solution of singular and stiff initial value problems. The integrators derived cope effectively well with stiff and singular initial value problems in ordinary differential equations. The methods in this class of integrators have been shown to be A and L stable. The implementation of the class of integrators on digital computers especially Pentium series was exhaustively analyzed in this work. A package in Fortran 70 was developed for easy implementation of results.