A trigonometrically fitted intra-step block Falkner method for the direct integration of second-order delay differential equations with oscillatory solutions

An intra-step block Falkner method whose coefficients depend on a parameter ? and the step length h is presented in this study for solving numerically second-order delay differential equations with oscillatory solutions. In the development of the method, the collocation and interpolation techniques were employed. The investigation of the properties of the method has shown that it is zero-stable and consistent, and consequently, convergent. The application of the method to some standard problems from the scientific literature show that it produced very accurate results.