Abstract: Based on the analysis of effects of time step-size on numerical solutions,this paper showed the necessity of step-size adaptation.Based on the relationship between error and step-size,two-step adaptation methods for solving initial value problems（IVPs） were introduced.They are Two-Step Method and Em-bedded Runge-Kutta Method.PRKEs were solved by implicit Euler method with step-sizes optimized by using Two-Step Method.It was observed that the control error has important influence on the step-size and the accuracy of solutions.With suitable control errors,the solutions of PRKEs computed by the above mentioned method are accurate reasonably.The accuracy and usage of MATLAB built-in ODE solvers ode23 and ode45,both of which adopt Runge-Kutta-Fehlberg method,were also studied and discussed.