Variable-coefficient BDF methods with fully-geometric grid for linear nonhomogeneous neutral pantograph equations

Abstract

This paper deals with numerical computation and analysis for the initial value problems (IVPs) of linear nonhomogeneous neutral pantograph equations. For solving this kind of IVPs, a class of extended k-step variable-coefficient backward differentiation formula (BDF) methods with fully-geometric grid are constructed. It is proved under the suitable conditions that an extended k-step variable-coefficient BDF method can arrive at k-order accuracy and is asymptotically stable. With a series of numerical experiments, the computational effectiveness and theoretical results of the presented methods are further confirmed.