Some procedures for the construction of high-order exponentially fitted Runge-Kutta-Nyström methods of explicit type (Q743360)

The paper is devoted to the construction of high-order exponentially fitted Runge-Kutta-Nyström methods for solving non-stiff systems of oscillatory ordinary differential equations. Two methods are proposed, allowing to explicitly determine both a fixed step size and a variable step method. The construction asserts that the desired stability and convergence properties are satisfied.