A New Methodology for the Development of Efficient Multistep Methods for First-Order Initial Value Problems with Oscillating Solutions: III the Role of the Derivative of the Phase Lag and the Derivative of the Amplification Factor

Abstract

Recently, the author developed a theory for the computation of the phase lag and amplification factor for explicit and implicit multistep methods for first-order differential equations. In this paper, we will investigate the role of the derivatives of the phase lag and the derivatives of the amplification factor on the efficiency of the newly developed methods. We will also present the stability regions of the newly developed methods. We will also present numerical experiments and conclusions on the newly developed methodologies.

Keywords

• numerical solution
• initial value problems (IVPs)
• Adams–Bashforth methods
• trigonometric fitting
• multistep methods