A new four-step implicit linear eight algebraic order method with vanished phase-lag and its first, second and third derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the one-dimensional radial Schrödinger equation and related problems. In order to produce an efficient multistep method the phase-lag property and its derivatives are used. An error analysis and a stability analysis is also investigated and a comparison with other methods is also studied. The efficiency of the new methodology is proved via theoretical analysis and numerical applications.

A new four-step implicit linear sixth algebraic order method with vanished phase-lag and its first derivative is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the one-dimensional radial Schrödinger equation and related problems. In order to produce an efficient multistep method the phase-lag property and its derivatives are used. The new method is analyzed for accuracy and periodicity properties, the error constants and interval and region of periodicity are investigated and obtained. The methods are compared with existing methods and they are tested on five problems from the literature.