New insights in the development of Numerov-type methods with minimal phase-lag for the numerical solution of the Schrodinger 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 e ight and ten. The methods have new features; namely that they are dissipati ve, i.e. they are not symmetric and they have no interval of periodicity. N umerical illustrations using (i) the radial Schrodinger equation and (ii) c oupled differential equations arising from the Schrodinger equation, indica te that these new methods are more efficient than older ones. It is seen th at the property of the phase-lag is more important than the non-empty inter val of periodicity in constructing numerical methods for the solution of th e Schrodinger equations and related problems. (C) 2001 Elsevier Science Ltd . All rights reserved.