Stability analysis of linear multistep methods for delay differential equations

Abstract

Stability properties of linear multistep methods for delay differential equations with respect to the test equation urn:x-wiley:01611712:media:ijmm768965:ijmm768965-math-0001 0 < λ < 1, are investigated. It is known that the solution of this equation is bounded if and only if | a | < − b and we examine whether this property is inherited by multistep methods with Lagrange interpolation and by parametrized Adams methods.