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A New Stable Algorithm to Compute hankel Transform Using Chebyshev Wavelets

Communications in Computational Physics 2010年第7期8卷 351-373页

作者： Rajesh K.Pandey Vineet K.Singh Om P.Singh PDPM Indian Institute of Information Technology Design and Manufacturing JabalpurIndia Birla Institute of Technology and Science-Pilani Goa CampusGoaIndia Department of Applied Mathematics Institute of TechnologyBanaras Hindu UniversityVaranasiIndia

A new stable numerical method,based on Chebyshev wavelets for numerical evaluation of hankel transform,is proposed in this *** Chebyshev wavelets are used as a basis to expand a part of the integrand,r f(r),appearing in the hankel transform *** transforms the hankel transform integral into a Fourier-Bessel *** truncating the series,an efficient and stable algorithm is obtained for the numerical evaluations of the hankel transforms of order ν>−*** method is quite accurate and stable,as illustrated by given numerical examples with varying degree of random noise terms εθ_(i) added to the data function f(r),where θ_(i) is a uniform random variable with values in[−1,1].Finally,an application of the proposed method is given for solving the heat equation in an infinite cylinder with a radiation condition.

关键词： hankel transforms Bessel functions Chebyshev wavelets random noise term

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The Green

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Acta Seismologica Sinica(English Edition) 2001年第2期14卷 196-202页

作者： LU Jian-fei Jiangsu University of Science and Technology Zhenjiang China Shanghai Jiaotong University Shanghai China

By using integral transform methods, the Green’s functions of horizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equations in frequency domain are established through the use of hankel integral transforms technique. Utilizing the above-mentioned general solutions, and the boundary conditions of the surface of the half-space and the continuous conditions at the plane of the horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse hankel transforms method, the Green’s functions of the harmonic horizontal force are obtainable. The degenerate case of the results deduced from this paper agrees well with the known results. Two numerical examples are given in the paper.

关键词： Biot theory hankel transforms Green’s function asymmetric P315.9

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AXISYMMETRIC BOUNDARY-VALUE PROBLEMS IN A PIEZOELECTRIC MEDIUM

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Acta Mechanica Solida Sinica 1998年第2期11卷 104-112页

作者： Zheng Bailin Wang Zikun Ji Xing Tongji Univ Dept Engn Mech & Technol Shanghai 200092 Peoples R China Xian Jiao Tong Univ Dept Mech Engn Xian Peoples R China

Based on the general solution of three-dimensional problems inpiezoelectric medium, with the method of Green's functins~[2],axisymmetric boundary-value problems are discussed. The purpose ofthis research is for analyzing the effective on mechanics andelectricity of the piezoelectric ceramics caused by voids andinclusions. The displacement, traction and electric Green's functionscorresponding to circular ring loads acting in the interior of apiezoelectric ceramic are obtained. A cylindrical coordinate systemis employed and hankel transform are applied with respect to radialcoor- dinates. Explicit solutions for Green's functions are presentedin terms of infinite integrals of Lipshitz- hankel type. By solving atraction boundary-value problem, the solution scheme is illustrate.

关键词： piezoelectric ceramics voids and inclusions hankel transforms

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