A P-stable exponentially-fitted method for the numerical integration of the Schrödinger equation

Abstract

In this paper we present a P-stable exponentially-fitted four-step method for the numerical integration of the radial Schrödinger equation. More specifically we present a method than satisfies the property of P-stability and also integrates exactly any linear combination of the functions {1, x, exp( ± w x), x exp( ± w x), x ²exp( ± w x)}. We tested the efficiency of our newly developed scheme against well known methods, with excellent results. The numerical illustration showed that our method is considerably more efficient compared to well‐known methods used for the numerical integration of resonance problem of the radial Schrödinger equation.

Keywords:

• Numerical solution
• Schrödinger equation
• Linear multistep methods
• P-stability
• Exponential fitting
• Trigonometric fitting

Keywords:

• 0.260
• 95.10.E;

Keywords:

• 65L05
• 65L06

Notes

†Active Member of the European Academy of Sciences and Arts, Corresponding Member of the European Academy of Sciences and Corresponding Member of European Academy of Arts, Sciences and Humanities

¹ In the case of the radial Schrödinger equation the frequency of the problem is equal to:

Additional information

Notes on contributors

T. E. Simos

† †Active Member of the European Academy of Sciences and Arts, Corresponding Member of the European Academy of Sciences and Corresponding Member of European Academy of Arts, Sciences and Humanities