High-Order Adams–Bashforth Methods for First-Order IVPs with Oscillating Solutions - Hong, Mei; Lin, Chia-Liang; Simos, Theodore E. (Mediterranean journal of mathematics, 2025)
The theory for computing the phase-lag and amplification-factor for both explicit and implicit multistep approaches for first-order differential equations was recently established by one of the authors. The goal of this work is to design high order Adams–Bashforth algorithms that eliminate the phase-lag, amplification-factor, and their respective derivatives. The stability zones of the recently developed approaches will also be presented. Additionally, we will discuss our findings from numerical experiments using the recently created techniques.