A generator of high-order embedded P-stable methods for the numerical solution of the Schrِdinger equation

A generator of new embedded P-stable methods of order 2n+2, where n is the number of layers used by the embedded methods, for the approximate numerical integration of the one-dimensional Schrِdinger equation is developed in this paper. These new methods are called embedded methods because of a simple natural error control mechanism. Numerical results obtained for one-dimensional differential equations of the Schrِdinger type show the validity of the developed theory.