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Zbl 0863.65042
Avdelas, G.; Simos, T.E.
A generator of high-order embedded $P$-stable methods for the numerical solution of the Schrödinger equation. (English)
[J] J. Comput. Appl. Math. 72, No.2, 345-358 (1996). ISSN 0377-0427

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.
[Z.Jackiewicz (Tempe)]

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
34L40 Particular ordinary differential operators
65L70 Error bounds (numerical methods for ODE)
65L20 Stability of numerical methods for ODE

Keywords: $P$-stability; phase shift problem; numerical examples; Schrödinger equation; embedded methods; error control

Cited in: Zbl 0930.65082

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