A Class of Two-Dimensional Dual Integral Equations and Its Application

FAN Tian-you; SUN Zhu-feng

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FAN Tian-you, SUN Zhu-feng. A Class of Two-Dimensional Dual Integral Equations and Its Application[J]. Applied Mathematics and Mechanics, 2007, 28(2): 225-230.

Citation:

FAN Tian-you, SUN Zhu-feng. A Class of Two-Dimensional Dual Integral Equations and Its Application[J]. Applied Mathematics and Mechanics, 2007, 28(2): 225-230.

Citation:

FAN Tian-you, SUN Zhu-feng. A Class of Two-Dimensional Dual Integral Equations and Its Application[J]. Applied Mathematics and Mechanics, 2007, 28(2): 225-230.

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A Class of Two-Dimensional Dual Integral Equations and Its Application

Department of Physics, Beijing Institute of Technology, Beijing 100081, P. R. China

Received Date: 2006-04-03
Rev Recd Date: 2006-11-30
Publish Date: 2007-02-15

Abstract

Abstract

Because exact analytic solution was not available,the double expansion and boundary collocation were used to construct an approximate solution for a class of two-dimensional dual integral equations in mathematical physics.The integral equations by this pr ocedure were reduced to infinite algebraic equations.The a ccuracy of the solution lies in the boundary collocation technique.The application of which for some complicated initial-boundary value problems in solidme chanics indicates the method is powerful.
- two-dimensional dual integral equations,
- double expansion,
- boundary collocation

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References(14)

References

[1]	Titchmarsh B C.Introduction to the Theory of Fourier Integrals[M].Oxford: Clarenden Press, 1937.
[2]	Busbridge I W.Dual integral equations[J].Math Soc Proc,1938,44(2):115-129. doi: 10.1112/plms/s2-44.2.115
[3]	Weber H.ber die Besselschen Funktionen und ihre Anwendung auf die Theorie der electrischen Strme[J].Journal für die Reihe und Angewandte Mathematik,1873,75(1)：5-105.
[4]	McDonald H M. The electrical distribution induced on a circular disk placed in any field of force[J].Phil Mag,1895,26(1)：257-260.
[5]	King L V. On the acoustic radiation pressure on circular disk[J].Roy Soc London Proc Ser A,1935,153(1):1-16. doi: 10.1098/rspa.1935.0218
[6]	Copson E T. On the problem of the electrified disk[J].Edinburgh Math Soc Proc,1947,8(1)：5-14.
[7]	Tranter C J. On some dual integral equations [J].Quar J Math Ser 2,1951,2(1):60-66. doi: 10.1093/qmath/2.1.60
[8]	Gordon A N. Dual integral equations[J].London Math Soc J,1954,29(5):360-369. doi: 10.1112/jlms/s1-29.3.360
[9]	Nobel B.On some dual integral equations[J].Quar J Math,1955,6(2)：61-67.
[10]	Nobel B.The solutions of Bessel-function dual integral equations by a multiplying factor method[J].Proceeding of Cambridge Philosophical Society,1963,59(4):351-362. doi: 10.1017/S0305004100036987
[11]	范天佑.对偶积分方程与对偶积分方程组及其在固体力学和流体力学中的某些应用[J].应用数学学报，1979,2(3)：212-230.
[12]	Fan T Y,Hahn H G,Violet A.Three-dimensional problem of transient contact dynamics[J].Science in China A,1996,39(10)：1096-1105.
[13]	Sun Z F, Wu X F,Fan T Y. Three-dimensional elliptic crack under impact loading[J].Acta Mechanica Solida Sinica,2001,14(4)：312-318.
[14]	范天佑.Laplace变换的数值反演[J].数学认识与实践,1987,16(3)：68-75.