Some stiffly stable second derivative continuous linear multistep methods with a hybrid point for stiff IVPS in ODEs

Abstract

Based on Gear¡¦s fixed step size backward differentiation methods, Gear (1968), second derivative continuous linear multistep methods with an off-step point are presented. This type of methods provides a means of bypassing the order barriers imposed by Dahlquist (1963) and also provides continuous solutions of IVPs in ODEs. The stiff stability of these methods is determined by using the boundary locus. Instability sets in at k ƒ­10 . Numerical results of the methods solving a non-linear and a linear stiff initial value problems in ordinary differential equations are compared to that of the state -of -the-art code, ODE 15s in MATLAB.