A new two–step implicit linear Obrechkoff twelfth algebraic order method with vanished phase–lag and its first, second, third and fourth 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. This algorithm belongs in the category of the multistep methods. In order to produce an efficient multistep method the phase–lag property and its derivatives are used. An error analysis and a stability analysis are 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.
