Numerical solution of Schrodinger equation using compact finite differences method and the cubic spline functions

  • Authors

    • Behnam Sepehrian Arak university
    • Marzieh Karimi Radpoor Islamic Azad University
    2014-11-22
    https://doi.org/10.14419/ijamr.v3i4.3743
  • Compact finite difference, Cubic Spline functions, Numerical solution, Schrodinger equation.

  • Abstract

    In this paper, a high-order method for solving the Schrodinger equation is introduced. We apply a compact finite difference approximation for discretizing spatial derivatives and we use the C1-cubic spline collocation method for the time integration of the resulting linear system of ordinary differential equations. The proposed method has fourth-order accuracy in both space and time variables. We can obtain both pointwise approximations at the all mesh points and, a cubic spline solution in each space step by the method. Numerical results show that the method is an efficient technique for solving the one-dimensional Schrodinger equation. 

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  • How to Cite

    Sepehrian, B., & Karimi Radpoor, M. (2014). Numerical solution of Schrodinger equation using compact finite differences method and the cubic spline functions. International Journal of Applied Mathematical Research, 3(4), 572-578. https://doi.org/10.14419/ijamr.v3i4.3743

    Received date: 2014-10-20

    Accepted date: 2014-11-09

    Published date: 2014-11-22