Some new variable-step methods with minimal phase lag for the numerical integration of special second-order initial-value problem

摘要

Two new variable step methods with minimal phase lag are developed for the numerical integration of the special second-order initial-value problem. An application to the one- dimensional Schrödinger equation on the phase-shift problem indicates that these new methods are generally more accurate than other previously developed finite difference methods, especially in the case of the high energies.