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A generator of high-order embedded P-stable methods for the numerical solution of the Schrödinger equation. (English) Zbl 0863.65042
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 Schrödinger equation is developed. 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 Schrödinger type show the validity of the developed theory.

MSC:
65L05Initial value problems for ODE (numerical methods)
34L40Particular ordinary differential operators
65L70Error bounds (numerical methods for ODE)
65L20Stability and convergence of numerical methods for ODE