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Stabilization Of A Four-Step Exponentially-Fitted Method And Its Application To The Schrödinger Equation

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  • T. E. SIMOS

    (Department of Computer Science and Technology, University of Peloponnese, GR-22 100 Tripolis, Greece)

Abstract

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.

Suggested Citation

  • T. E. Simos, 2007. "Stabilization Of A Four-Step Exponentially-Fitted Method And Its Application To The Schrödinger Equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 315-328.
    • Handle: RePEc:wsi:ijmpcx:v:18:y:2007:i:03:n:s0129183107009261
    DOI: 10.1142/S0129183107009261
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    Cited by:

    1. Shokri, Ali & Mehdizadeh Khalsaraei, Mohammad, 2020. "A new family of explicit linear two-step singularly P-stable Obrechkoff methods for the numerical solution of second-order IVPs," Applied Mathematics and Computation, Elsevier, vol. 376(C).

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