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Solving algorithm for inverse problem of partial differential equation parameter identification based on IGEP

  • Feng Baolin
Article
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Abstract

Gene expression programming (GEP) is a mathematical model that can be used to optimize complex systems. It has not only limited to specific problems, but also has good robustness in solving various problems, which has been applied in many disciplines such as biochemistry, physics, and mathematics. In this paper, the IGEP algorithm was proposed based on the optimization of GEP algorithm, and the algorithm for solving the inverse problem of parameter identification of partial differential equations based on this algorithm was studied. The structure and steps of GEP algorithm were analyzed firstly, and the GEP (IGEP) based on improved mutation operator was proposed. The algorithm advantage of IGEP for solving the inverse problem of partial differential equations was discussed. In addition, the simulation experiments were carried out to prove the feasibility and superiority of the proposed algorithm.

Keywords

IGEP Partial differential equation Parameter identification inverse problem Solving algorithm Research 

Notes

Acknowledgements

The study was supported by “Science and Technology Project of China Railway Corporation, China (Grant No. 1341324011)” and “National key innovation prediction project of Mudanjiang Normal University (Grant No. GY201205)”.

References

  1. 1.
    Chen, Y., Li, K., Chen, Z., et al.: Restricted gene expression programming: a new approach for parameter identification inverse problems of partial differential equation. Soft. Comput. 21(10), 1–13 (2017)Google Scholar
  2. 2.
    Guo, P., Wu, X., Wang, L.B.: Multiple soliton solutions for the variant Boussinesq equations. Adv. Differ. Equ. 2015(1), 37 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Denisov, A.M.: Inverse problem for a quasilinear system of partial differential equations with a nonlocal boundary condition containing a retarded argument. Differ. Equ. 51(9), 1126–1136 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Pintarelli, M.B.: Linear partial differential equations of first order as bi-dimensional inverse moments problem. Appl. Math. 6(6), 979–989 (2015)CrossRefGoogle Scholar
  5. 5.
    Denisov, A.M.: Integral equations related to the study of an inverse coefficient problem for a system of partial differential equations. Differ. Equ. 52(9), 1142–1149 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Zhang, W., Sun, Z., Wang, Z., et al.: A coupled model of partial differential equations for uranium ores heap leaching and its parameters identification. J. Inverse Ill-posed Probl. 24(1), 41–50 (2015)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Pintarelli, M.B.: Parabolic partial differential equations as inverse moments problem. Appl. Math. 07(1), 77–99 (2017)CrossRefGoogle Scholar
  8. 8.
    Liu, T.: A wavelet multiscale-homotopy method for the parameter identification problem of partial differential equations. Comput. Math. Appl. 71(7), 1519–1523 (2016)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Groh, A., Kohr, H., Louis, A.K.: Numerical rate function determination in partial differential equations modeling cell population dynamics. J. Math. Biol. 74(3), 1–33 (2016)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Gepreel, K.A., Nofal, T.A.: Extended trial equation method for nonlinear partial differential equations. Zeitschrift Für Naturforschung A 70(4), 269–279 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate School of Mudanjiang Normal UniversityHelongjiangChina

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