文摘
In the present paper we will develop and analyse a new five-stages symmetric two-step method of high algebraic order with vanished phase-lag and its first, second, third, fourth and fifth derivatives. We will construct the new method. We will compute its local local truncation error (LTE). We will produce the asymptotic form of the LTE applying the new method to the radial time independent Schrödinger equation and we will compare it with other asymptotic forms of LTE of similar methods. Applying the new method to a scalar test equation with frequency different than the frequency of the scalar test equation used for the phase-lag analysis, we will investigate the stability and the interval of periodicity of the new method based and we will compare the produced interval of periodicity with other intervals of similar methods. Finally, we will examine the effectiveness of the new method applying it to the coupled Schrödinger equations.