ABSTRACT
This chapter explores the concept of stability with respect to Runge–Kutta (RK) methods and the property of stiffness, in relation to systems of differential equations. It considers special RK methods for application to such systems. The foregoing introductory treatment of absolute stability is based on a scalar test problem which is much simpler than one which usually demands numerical treatment. Actually the region within which absolute stability is assured is symmetric about the real axis, and so it is customary to display only the positive imaginary half-plane. A further point to note is that the stability of a numerical solution does not imply its high accuracy. Absolute stability ensures that a numerical solution will be bounded but it may differ quite significantly from the true solution. It should be emphasised that one requires a method to be absolutely stable only for problems with decreasing solution components.
