A special family of parameter dependent nested hybrid multistep methods for stiff ODEs

Abstract

In this paper, we introduce a special family of parameter dependent nested hybrid linear multistep methods (PDNHLMMs) for the numerical integration of stiff initial value problems (IVPs) in ordinary differential equations (ODEs). Hybrid method is incorporating one or more off-step points for better stability properties and higher order than the conventional linear multistep methods (LMM). This type of methods provides a means of bypassing the Dahlquist order and stability barrier of the conventional LMM. The proposed method is A- stable and A (α) –stable for step number k ≤ 6. Numerical experiment shows that the new parameter dependent formulae compete favorably well with other existing methods in the literature.