Optimized Runge-Kutta pairs for problems with oscillating solutions

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Fitted modifications of classical Runge‐Kutta pairs of orders 5(4) (2018, methodology): “Then (5) holds, and ~δðvÞ, ~δ0ðvÞ, and η(v) are given by the following expressions: TABLE 1 The coefficients of the 5(4) pair in consideration”
A family of explicit linear six-step methods with vanished phase-lag and its first derivative (2014, methodology): “(see for more details [1–121] and references therein).”
High order closed Newton-Cotes exponentially and trigonometrically fitted formulae as multilayer symplectic integrators and their application to the radial Schrödinger equation (2012, methodology): “The aim and scope of this research is the construction of fast and reliable algorithms for the solution of the Schrödinger equation and related problems (see for example [4–127]).”
High algebraic order methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation (2010, unknown): “In [ 25 ] the authors have obtained three types of methods for the numerical solution of IVPs with periodical solution.”