New insights in the development of Numerov-type methods with minimal phase-lag for the numerical solution of the Schrödinger equation.
Explicit Numerov-type methods with minimal phase-lag are developed in this paper. These methods are of algebraic order five and have phase-lag order eight and ten. The methods have new features; namely that they are dissipative, i.e. they are not symmetric and they have no interval of periodicity. Numerical illustrations using (i) the radial Schrödinger equation and (ii) coupled differential equations arising from the Schrödinger equation, indicate that these new methods are more efficient than older ones. It is seen that the property of the phase-lag is more important than the non-empty interval of periodicity in constructing numerical methods for the solution of the Schrödinger equations and related problems.
Simos
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TE
Department of Civil Engineering, School of Engineering, Democritus University of Thrace, Xanthi, Greece. tsimos@mail.ariadne-t.gr
Williams
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PS