In this paper, we construct an embedded pair based on trigonometrically fitted two-step hybrid methods (THM) for solving oscillatory problems. The coefficients of the new method are variables depending on frequency of the problem and step-size of integration. Preservation of algebraic order of the base methods is verified. Numerical experiment is conducted via integration of a variety of test problems with known solutions, where efficiency and accuracy of the method are measured alongside some existing codes in the literature. Results obtained reveal that the new method is more promising than the existing codes considered in the paper.

numerical integration, trigonometrically fitting, variable coefficients, hybrid methods, oscillatory problems.