Linear multistep methods with variable matrix coefficients

Abstract

A class of linear multistep methods with variable matrix coefficients for integration of systems of ordinary differential equations (I.V.P.) is introduced. The asymptotic behaviour of the numerical solution as we use the class for integration of the time dependent linear system $\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{y} ' = A(t)\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{y}$ is established for a third order subclass. This shows how instability effects arising from the "spurious" roots of the multistep method may be effectively suppressed if certain stabilizing conditions are satisfied.