On the Regularization Method of the First Kind Fredholm Integral Equation With a Complex Kernel and its Application

You Yunxiang; Miao Guoping

Volume 19 Issue 1

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Article Navigation > Applied Mathematics and Mechanics > 1998 > 19(1): 70-78

You Yunxiang, Miao Guoping. On the Regularization Method of the First Kind Fredholm Integral Equation With a Complex Kernel and its Application[J]. Applied Mathematics and Mechanics, 1998, 19(1): 70-78.

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On the Regularization Method of the First Kind Fredholm Integral Equation With a Complex Kernel and its Application

Shanghai Jiao Tong University, Shanghai 200030, P. R. China

Received Date: 1996-06-24
Rev Recd Date: 1997-06-08
Publish Date: 1998-01-15

Abstract

Abstract

The regularized integrodifferential equation for the first kind Fredholm integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate rgeularized solutions is discussed. As an application of the method, an inverse problem in the two-demensional wave-making problem of a flat plate is solved numerically, and a practical approach of choosing optimal regularization parameter is given.
- Inverse problem,
- Fredholm integral equation of the first kind,
- complex kernel,
- regularization method

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References(10)

References

[1]	J.Baumeister,Stable Solution of Inverse Problem,Vieweg & Ohn,Braunschweig/Wiesbaden(1987).
[2]	P.C.Sabatier(ed),Inverse Pr oblems :An In ter disciplinary Study,Academic Press Boston(1987).
[3]	A.N.Tikhonov and V.Y.Arsenin,Solution of Ill-posed Pr oblems,Wiley,New York(1977).
[4]	R.Kress,Linear Intergral Equations,Springer-Verlag,Berlin(1989).
[5]	A.N.Tikhonov,On solution of incorrectly formulated problems and the regularization method,Sovier Math.Doklady,4(1963),1035-1038.(English version)
[6]	D.L.Phillips,A technique for the numerical solution of certain intergral equations of the first kind,J.Ass.Comp.Math.,9(1962),84-97.
[7]	E.Schock,On the asymptotic order of accuracy of Tikhonov regularization,J.Optim.Theroy Appl.,44(1984),95-104.
[8]	缪国平、刘应中编,《海洋工程水动力学基础》,海洋出版社,北京(1991).
[9]	缪国平、刘应中,有限水深表面压力脉动产生的速度势与二阶绕射问题的辐射条件,中国造船,总107期(1989),1-13.
[10]	李世雄、刘家绮编,《小波变换和反演数学基础》,地质出版社,北京(1994).

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