One Step Adapted Hybrid Second Derivative Block Method for Initial Value Problems with Oscillating Solutions

The purpose of this study is to develop a one-step block hybrid formula for solving a system of first-order differential equations with oscillating solutions. The formula is designed to avoid the problems that come with the conventional hybrid formulas. To increase accuracy, the formula incorporates the second order derivative into its construction. The construction of the formula is on the assumption that when the real solution is a linear combination of polynomial and sinusoidal functions that includes a parameter, it causes no errors. The formula is a sixth-order convergence, according to the analysis. The proposed formula’s performance is demonstrated using some typical numerical examples from recent literature whose solutions exhibit oscillatory behavior.