Stable linear multistep methods with off-step points for the solution of ordinary differential equations

Abstract

Of recent, stability has become an important concept and a qualitative property in any numerical integration scheme. In this work, we propose two stable linear multistep methods with off-step points for the numerical integration of ordinary differential equations whose development is collocation and interpolation based. The boundary locus techniques show that the proposed schemes are zero-stable, A-stable and  -stable for some step number and are found suitable for stiff differential equations. Numerical results obtained compare favourably with some existing methods in literature.