Optimized Explicit Symmetric Linear Multistep Methods for the Numerical Solution of the Schrodinger Equation and Related Orbital Problems

摘要

We develop two new optimized explicit symmetric linear multistep methods with phase-lag order eight and infinite (phase-fitted), for the efficient numerical solution of the radial time-independent Schrodinger equation during the resonance problem with the use of the Woods-Saxon potential. It can also be used to integrate related initial value problems with oscillating solutions such as orbital problems. The new phase-fitted method has improved interval of periodicity as compared to the corresponding classical method with constant coefficients and other methods from the literature. We also apply the methods along with other known methods to real periodic problems, in order to measure their efficiency.