A number of techniques and solvers have been suggested, developed, and described, but a clear definition of stiffness has not been provided. In this paper, an analysis of the A-stable implicit Runge-Kutta methods is undertaken using stability function and the region of absolute stability, which shows region of each of the methods. Also to compare various stiff solvers based on their region of absolute stability. It helps a stiff ordinary differential equation solver, to identify appropriate numerical methods with unbounded region of absolute, appropriate for stiff problems solving.