A Parametric Six-Step Method For Second Order IVPs With Oscillating Solutions

In this paper, we have developed an explicit symmetric six-step method. This new method is phase-fitted and incorporates a free coefficient as a parameter. Using a wide range of values for this parameter, we computationally define the periodicity interval. Numerical outcomes guided us toward identifying optimal values for the parameter, establishing the new method’s high efficiency. The efficiency of the new method is demonstrated through its application to oscillatory problems, comparing it with well-known phase-fitted methods.