Skip to main content
SpringerLink
Log in

Numerical approach for a system of second kind Volterra integral equations in magneto-electro-elastic dynamic problems

  • Piezoelectricity, Acoustic Waves and Devices Applications
  • Published:
Journal of Zhejiang University-SCIENCE A Aims and scope Submit manuscript

Abstract

The elastodynamic problems of magneto-electro-elastic hollow cylinders in the state of axisymmetric plane strain case can be transformed into two Volterra integral equations of the second kind about two functions with respect to time. Interpolation functions were introduced to approximate two unknown functions in each time subinterval and two new recursive formulae are derived. By using the recursive formulae, numerical results were obtained step by step. Under the same time step, the accuracy of the numerical results by the present method is much higher than that by the traditional quadrature method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Brunner, H., van der Houwen, P.J., 1986. The numerical solution of Volterra equations: CWI monographs, North-Holland, Amsterdam.

    Google Scholar 

  • Christopher, T.H., Baker, M.A., 1977. The Numerical Treatment of Integral Equation. Oxford University Press, Oxford.

    MATH  Google Scholar 

  • Delves, L.M., Mohamed, J.L., 1985. Computational Method for Integral Equations. Cambridge University Press, Cambridge.

    Book  MATH  Google Scholar 

  • Ding, H.J., Wang, H.M., Chen, W.Q., 2004. Numerical method for Volterra integral, equation of the second kind in piezoelectric dynamic problems.Appl. Math. Mech.,25(1):16–23.

    Article  MATH  Google Scholar 

  • Hou, P.F., Leung, A.Y.T., 2004. The transient responses of magneto-electric-elastic hollow cylinders.Smart Mater. Struct.,13(4):762–776.

    Article  Google Scholar 

  • Kress, R., 1989. Linear Integral Equation. Springer-Verlag, Berlin.

    Book  MATH  Google Scholar 

  • Li, H.X., Wang, G.J., Wang, C.Z., 1995. Exact solutions of several classes of integral equations of Volterra type and ordinary differential equations.Journal of Shanghai Institute of Railway Technology,16(1):72–85 (in Chinese).

    MathSciNet  Google Scholar 

  • Maleknejad, K., Shahrezaee, M., 2004. Using Runge-Kutta method for numerical solution of the system of Volterra integral equation.Appl. Math. Comput,149(2):399–410.

    MathSciNet  MATH  Google Scholar 

  • Maleknejad K., Aghazadeh, N., 2005. Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method.Appl. Math. Comput,161(3):915–922.

    MathSciNet  MATH  Google Scholar 

  • Oja, P., Saveljeva, D., 2002. Cubic spline collocation for Volterra integral equations.Computing,69(4):319–337.

    Article  MathSciNet  MATH  Google Scholar 

  • Yan, Y.B., Cui, M.G., 1993. The exact solution of the second kind Volterra integral equation.Numerical Mathematics—A Journal of Chinese University,15(4):291–296 (in Chinese).

    MathSciNet  MATH  Google Scholar 

  • Zerarka, A., Soukeur, A., 2005. A generalized integral quadratic method: I. An efficient solution for one-dimensional Volterra integral equation.Communications in Nonlinear Science and Numerical Simulation,10(6):653–663.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Zhejiang University, 310027, Hangzhou, China

    Ding Hao-jiang

  2. Department of Mechanics, Zhejiang University, 310027, Hangzhou, China

    Wang Hui-ming

Authors
  1. Ding Hao-jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wang Hui-ming
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Project supported by the National Natural Science Foundation of China (No. 10472102) and Postdoctoral Foundation of China (No. 20040350712)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hao-jiang, D., Hui-ming, W. Numerical approach for a system of second kind Volterra integral equations in magneto-electro-elastic dynamic problems. J Zheijang Univ Sci A 6, 928–932 (2005). https://doi.org/10.1631/jzus.2005.A0928

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1631/jzus.2005.A0928

Keywords

Document code

CLC number

Search

Navigation