An Embedded Explicit Hybrid Method for Ordinary Differential Equations

Problem statement: Many differential systems that appear in practice were special second-order ordinary differential equations of the form y" = f (x, y). In the past research, there was a continuous need for methods for numerically solving these equations. Approach: This study describes the derivation and implementation of a pair of embedded explicit hybrid methods for solving non-stiff second-order ordinary differential equations y" = f (x, y). Results: It was shown that our method was more efficient than the well-known embedded pair of explicit runge-kutta-nystrom methods for solving some second-order problems. Conclusion: Our method can be considered as an alternative for the numerical solution of y" = f (x, y).