A Hybrid Linear Collocation Multistep Scheme For Solving First Order Initial Value Problems

Abstract

This paper proposes a five-step ninth order hybrid linear multistep method with three non-step points for the solution of first order initial value problems(IVPs). The main method and additional methods are obtained from the same continuous scheme derived via interpolation and collocation procedure. The methods are then applied in block form as simultaneous numerical integrators over non-overlapping intervals. The schemes are consistent, zero stable, convergent and accurate.