Advanced Mathematical Models & Applications

This paper presents the development of new explicit modified hybrid methods for solving linear second-order ordinary differential equations numerically. Some coefficients of the proposed methods were derived by enforcing exact integration of sin⁡(wt) and cos⁡(wt), at each stage, while the remaining coefficients were adopted from the existing adapted Numerov scheme. The coefficients depend on v=wh, where w is the problem frequency and h the step size. The analysis of stability for the new methods was described. The methods were applied, under a constant step-size framework, to several linear second-order ODE problems. Numerical experiments demonstrate their superior performance compared to existing methods.