PREDICTOR CORRECTOR PHASE-FITTED METHODS FOR Y''=F(X,Y) AND AN APPLICATION TO THE SCHRODINGER EQUATION

摘要

Some phase-fitted P-stable methods are developed here. These methods have an algebraic order two and four, an interval of periodicity (O, infinity), and a phase-lag of order inifinity. Applications of the new methods to an orbit equation and the resonance problem of the Schrodinger equation (this problem involves finding all values of the energy for which the phase shift delta (E) is equal to pi/2) show that the new methods are much more efficient than are other well-known methods. Also, based on these two methods, a new variable-step technique is obtained. Application of the new variable-step scheme to the phase-shift problem of the radial Schrodinger equation and to close-coupled equations of the Schrodinger type shows that the new variable-step method is much more efficient than is the well-known method of Raptis and Cash. (C) 1995 John Wiley & Sons, Inc. [References: 20]