ABSTRACT
The importance of highly stable formulae for application to Stiff systems, in which is some special explicit Runge-Kutta (RK) methods were constructed. Unfortunately, the Adams-Moulton methods of increasing order still feature shrinking stability regions, making them quite unsuitable for Stiff problems. The chapter explores the important class of multistep methods, the backward differentiation formulae (BDF) with unlimited real absolute stability. Implicit multistep and RK processes require solutions of systems of non-linear algebraic equations at each step. In the RK case, the equations arise at each stage of the process. The iterative solution of these equations comprises the major computational cost in implementing all implicit schemes for Stiff systems. Although RK methods generally have better stability characteristics than multistep methods, the explicit methods considered so far cannot provide A-stability or even match the higher order BDFs in this respect.
