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Symplectic Schemes for Linear Stochastic Schrödinger Equations with Variable Coefficients

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Listed:
  • Xiuling Yin
  • Yanqin Liu

Abstract

This paper proposes a kind of symplectic schemes for linear Schrödinger equations with variable coefficients and a stochastic perturbation term by using compact schemes in space. The numerical stability property of the schemes is analyzed. The schemes preserve a discrete charge conservation law. They also follow a discrete energy transforming formula. The numerical experiments verify our analysis.

Suggested Citation

  • Xiuling Yin & Yanqin Liu, 2014. "Symplectic Schemes for Linear Stochastic Schrödinger Equations with Variable Coefficients," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:427023
    DOI: 10.1155/2014/427023
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    References listed on IDEAS

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    1. K. Ivaz & A. Khastan & Juan J. Nieto, 2013. "A Numerical Method for Fuzzy Differential Equations and Hybrid Fuzzy Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. K. Ivaz & A. Khastan & Juan J. Nieto, 2013. "A Numerical Method for Fuzzy Differential Equations and Hybrid Fuzzy Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, October.
    3. A. Ashyralyev & A. Hanalyev & P. E. Sobolevskii, 2001. "Coercive solvability of the nonlocal boundary value problem for parabolic differential equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 6(1), pages 53-61.
    4. W. M. Abd-Elhameed & E. H. Doha & Y. H. Youssri, 2013. "New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, October.
    5. W. M. Abd-Elhameed & E. H. Doha & Y. H. Youssri, 2013. "New Wavelets Collocation Method for Solving Second‐Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. A. Ashyralyev & A. Hanalyev & P. E. Sobolevskii, 2001. "Coercive solvability of the nonlocal boundary value problem for parabolic differential equations," Abstract and Applied Analysis, Hindawi, vol. 6, pages 1-9, January.
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