Full Text:   <1446>

CLC number: O347.1; O241.8

On-line Access: 

Received: 2005-02-05

Revision Accepted: 2005-06-03

Crosschecked: 0000-00-00

Cited: 3

Clicked: 3857

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.9 P.928~932

http://doi.org/10.1631/jzus.2005.A0928


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


Author(s):  DING Hao-jiang, WANG Hui-ming

Affiliation(s):  Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   wanghuiming@zju.edu.cn

Key Words:  Magneto-electro-elastic, Elastodynamic problem, Volterra integral equation, Numerical solution, Recursive formula


DING Hao-jiang, WANG Hui-ming. Numerical approach for a system of second kind Volterra integral equations in magneto-electro-elastic dynamic problems[J]. Journal of Zhejiang University Science A, 2005, 6(9): 928~932.

@article{title="Numerical approach for a system of second kind Volterra integral equations in magneto-electro-elastic dynamic problems",
author="DING Hao-jiang, WANG Hui-ming",
journal="Journal of Zhejiang University Science A",
volume="6",
number="9",
pages="928~932",
year="2005",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2005.A0928"
}

%0 Journal Article
%T Numerical approach for a system of second kind Volterra integral equations in magneto-electro-elastic dynamic problems
%A DING Hao-jiang
%A WANG Hui-ming
%J Journal of Zhejiang University SCIENCE A
%V 6
%N 9
%P 928~932
%@ 1673-565X
%D 2005
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2005.A0928

TY - JOUR
T1 - Numerical approach for a system of second kind Volterra integral equations in magneto-electro-elastic dynamic problems
A1 - DING Hao-jiang
A1 - WANG Hui-ming
J0 - Journal of Zhejiang University Science A
VL - 6
IS - 9
SP - 928
EP - 932
%@ 1673-565X
Y1 - 2005
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2005.A0928


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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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

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

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

[4] 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.

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

[6] Kress, R., 1989. Linear Integral Equation. Springer-Verlag, Berlin.

[7] 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).

[8] 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.

[9] 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.

[10] Oja, P., Saveljeva, D., 2002. Cubic spline collocation for Volterra integral equations. Computing, 69(4):319-337.

[11] 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).

[12] 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.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE