STABILIZATION OF A FOUR-STEP EXPONENTIALLY-FITTED METHOD AND ITS APPLICATION TO THE SCHR?DINGER EQUATION

摘要

In this paper we present a singularly P-stable exponentially — fitted four-step method for the numerical solution of the radial Schr?dinger equation. More specifically we present a method that is singularly P-stable (a concept later introduced in this paper) and also integrates exactly any linear combination of the functions {1, x, x2, x3, x4, x5, exp (±Ivx)}. The numerical experimentation showed that our method is considerably more efficient compared to well-known methods used for the numerical solution of resonance problem of the radial Schr?dinger equation.