A Third Order Small Parameter Method and Its Nordsieck Expression

A third order small parameter method and its Nordsieck expression are given in this paper. It is based on Gear's method of order 2 and order 3. For moderate stiff problems this method is suitable. In 1] we proposed a second order numerical method for stiff ODEs. The purpose of this paper is to raise the order from 2 to 3 and give its Nordsieck expression, making it automatically suit varying stepsize calculation.