A Four-Stage Fifth-Order Trigonometrically Fitted Semi-Implicit Hybrid Method for Solving Second-Order Delay Differential Equations

Abstract

We derived a two-step, four-stage, and fifth-order semi-implicit hybrid method which can be used for solving special second-order ordinary differential equations. The method is then trigonometrically fitted so that it is suitable for solving problems which are oscillatory in nature. The methods are then used for solving oscillatory delay differential equations. Numerical results clearly show the efficiency of the new method when compared to the existing explicit and implicit methods in the scientific literature.

Trigonometrically-Fitted Fifth Order Four-Step Predictor-Corrector Method for Solving Linear Ordinary Differential Equations with Oscillatory Solutions

“…The focus of the numerical solution of the above equation is the subject of extensive research activity over the last two decades (see [14,7,22,20,19,21,3,13,17]). Extensive reviews of the methods developed for the solution of (1) with oscillating behavior can be found in [19,21] and the references therein, Ibrahim and Ikhile [7], as well as [1,13,17].…”

“…To obtain a more accurate numerical results for problem (1), researchers have derived methods which take into account the nature of the problems to be solved. To do so they used fitting techniques such as phase-fitting, exponential and trigonometric fitting to enhance the efficiency of the original method.…”