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 Schrodinger 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.
