P-stability‎, ‎TF and VSDPL technique in Obrechkoff methods for the numerical solution of the Schrodinger equation

Many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. For the efficient solution of the above mentioned problems, linear multistep methods or Runge-Kutta technique are used. For the simulation of chemical procedures the radial Schrodinger equation is used frequently. In the present paper we will study a symmetric two-step Obrechkoff method, in which we will use of technique of VSDPL (vanished some of derivatives ofphase-lag), for the numerical integration of the one-dimensional Schrodinger equation. We will show superiority of new method in stability, accuracy and efficiency. So we present a stability analysis and an error analysis based on the radial Schrodinger equation. Also we will apply the new proposed method to the resonance problem of the radial Schrodinger equation.