A New Methodology for the Development of Efficient Multistep Methods for First-Order Initial Value Problems with Oscillating Solutions V: The Case of the Open Newton–Cotes Differential Formulae

Abstract

The author has just published a theory on first-order differential equations that accounts for the phase-lag and amplification-factor calculations using explicit, implicit, and backward differentiation multistep methods. Eliminating the phase-lag and amplification-factor derivatives, his presentation delves into how the techniques’ effectiveness changes. The theory for determining the phase lag and amplification factor, initially established for explicit multistep techniques, will be extended to the Open Newton–Cotes Differential Formulae in this work. The effect of the derivatives of these variables on the efficiency of these calculations will be studied. The novel discovered approach’s symplectic form will be considered next. The discussion of numerical experiment findings and some conclusions on the existing methodologies will conclude in this section.

Keywords

• numerical solution
• initial value problems (IVPs)
• open Newton–Cotes
• phase-fitting
• amplification-fitting
• derivative of the phase lag