A Linear Four-Step Method with Vanished Phase-Lag and its First and Second Derivatives for the Numerical Solution of Periodic Initial and/or Boundary Value Problems

摘要

A linear explicit four-step method with vanished phase-lag and its first and second derivatives for the numerical solution of second order initial or boundary-value problems with periodical and/or oscillating behavior of the solution is investigated in this paper. We base the construction of the new proposed method on the vanishing of the phase-lag and its first and second derivatives. A comparative local truncation error analysis with other similar methods of the literature is investigated. The stability analysis for the new obtained methos is also presented. The effectiveness of the new developed method is shown with an application of this method to the resonance problem of the one dimensional time independent Schrodinger equation.