A family of modified two-derivative Runge–Kutta (MTDRK) methods for the integration of the Schrödinger equation are obtained. Two new three-stage and fifth order TDRK methods are derived. The numerical results… Click to show full abstract
A family of modified two-derivative Runge–Kutta (MTDRK) methods for the integration of the Schrödinger equation are obtained. Two new three-stage and fifth order TDRK methods are derived. The numerical results in the integration of the radial Schrödinger equation with the Woods–Saxon potential are reported to show the high efficiency of our new methods. The results of the error analysis are illustrated by the resonance problem.
               
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