A new approach on the construction of trigonometrically fitted two step hybrid methods

The construction of trigonometrically fitted two step hybrid methods for the numerical solution of second-order initial value problems is considered. These methods are suitable for the numerical integration of problems with periodic or oscillatory behavior of the solution and have variable coefficients depending on the frequency of each problem. The modification of classical two step hybrid methods is done by inserting extra parameters at each stage. We derive the coefficients of the modified methods for the general case of s stages. As examples we present the modifications of three methods of algebraic orders five, six and seven.