Symplectic Methods for the Numerical Solution of the Radial Shrödinger Equation

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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).”
Exponentially and Trigonometrically Fitted Methods for the Solution of the Schrödinger Equation (2010, methodology): “–I n [26, 27, 60 , 61] some modified symplectic methods are developed.”
High order closed Newton-Cotes exponentially and trigonometrically fitted formulae as multilayer symplectic integrators and their application to the radial Schrödinger equation (2012, methodology): “– Symplectic integrators are studied in [54–80].”
Symplectic Methods of Fifth Order for the Numerical Solution of the Radial Shrödinger Equation (2004, methodology): “Methods used: (i) ‐♦‐: Yoshida [6] symplectic-scheme method of four stage-fourth order, (ii) ‐� ‐: Yoshida [6] symplectic-scheme method of eight stage‐six order, (iii) ‐ ×‐: symplectic-scheme of three stage-third order [ 7 ], (iv) ‐✷‐: new method with symplectic-scheme of seven stage-fifth order.”
An optimized explicit Runge-Kutta method with increased phase-lag order for the numerical solution of the Schrödinger equation and related problems (2009, methodology): “Many methods have been developed for the numerical approximation of the above problem (for more details see [1–49]).”