STABILIZATION OF A FOUR-STEP EXPONENTIALLY-FITTED METHOD AND ITS APPLICATION TO THE SCHRÖDINGER EQUATION

In this paper we present a singularly P-stable exponentially — fitted four-step method for the numerical solution of the radial Schrödinger 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 Schrödinger equation.

P-stable Four-Step Exponentially-Fitted Method for the Numerical Integration of the Schr¨odinger Equation

In this paper we present a P-stable exponentially-fitted four-step method for the numerical solution of the radial Schr¨odinger equation. More specifically we present a method than satisfies the property of P-stability and in the same time integrates exactly any linear combination of the functions {1, x, x2, x3, exp ± w x , x exp ± w x}. We tested the efficiency of our newly obtained scheme against well known methods, with excellent results. 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¨odinger equation.