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STRESS RATE integral equations OF ELASTOPLASTICITY

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Acta Mechanica Sinica 1996年第1期12卷 55-64页

作者：陈海波王有成吕品 Modern Mechanics Department University of Science and Technology of China Hefei 230026 China Department of Civil Engineering Hefei Polytechnic University Hefei 230009 China

The stress rate integral equations of elastoplasticity are deduced based on Ref. [1] by consistent methods. The point at which the stresses and/or displacements are calculated can be in the body or on the boundary, and in the plastic region or elastic one. The existence of the principal value integral in the plastic region is demonstrated strictly, and the theoretical basis is presented for the paticular solution method by unit initial stress fields. In the present method, programming is easy and general, and the numerical results are excellent.

关键词： the stress rate of inner point or boundary one integral equations boundary element techniques the particular solution method by unit initial stress fields

Uniqueness of Inversion Problems Described by First—Kind integral equations

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Chinese Physics Letters 2002年第2期19卷 147-149页

作者：徐铁峰 FacultyofInformationScienceandEngineering NingboUniversityNingbo315211

We propose a general method to prove the uniqueness of the inversion problems described by first-kind integral equations. The method depends on the analytical properties of the Fourier transform of the integral kernel and the finiteness of the total states (or probability, if normalized), the integration of the ``local'' density of states, which is a rather moderate condition and satisfied by many inversion problems arising from physics and engineering

关键词： integral equations

OPTIMIZATION OF ADAPTIVE DIRECT METHOD FOR APPROXIMATE SOLUTION OF integral equations OF SEVERAL VARIABLES

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Acta Mathematica Scientia 2004年第2期24卷 228-234页

作者：马万房艮孙 DepartmentofMathematics BeijingNormalUniversityBeijing100875China

This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic So... 详细信息

关键词： integral equations direct methods anisotropic sobolev classes

Optimization of Approximate Solution of integral equations of Several Variables

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Acta Mathematica Sinica,English Series 2002年第3期18卷 455-462页

作者： Wan MA Xing Hua WANG Department of Mathematics, Zhejiang University. Hangzhou 310028, P. R. China atho.imed.uni-erlangen.de

In this paper, we consider the problem of optimization of adaptive direct methods of operator equations. Adaptivity of a direct method is understood in the sense that the subspace on the basis of which it is constructed is chosen depending on the operator of the concrete equation (otherwise, nonadaptive direct method is then concerned), which would essentially let us increase the precision. For some classes of the second kind of Fredhlom integral equations with anisotropic smooth kernels we determine the exact order of the error of adaptive direct methods, and we also give an optimal algorithm.

关键词： integral equations Direct methods Anisotropic Sobolev classes

BOUNDARY integral equations FOR THE BENDING PROBLEM OF PLATES ON TWO-PARAMETER FOUNDATION

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Applied Mathematics and Mechanics(English Edition) 1992年第7期13卷 657-667页

作者：李正良邓安福 Chongqing Institute of Architecture and Engineering Chongqing

By means of Fourier integral transformation of generalized function, the fundamental solution for the bending problem of plates on two-parameter foundation is derived in this paper, and the fundamental solution is expanded into a uniformly convergent series. On the basis of the above work, two boundary integral equations which are suitable to arbitrary shapes and arbitrary boundary conditions are established by means of the Rayleigh-Green identity. The content of the paper provides the powerful theories for the application of BEM in this problem.

关键词： Bending (deformation) Boundary element method Convergence of numerical methods Fourier transforms integral equations

EPSILON-ALGORITHM AND ETA-ALGORITHM OF GENERALIZED INVERSE FUNCTION-VALUED PAD APPROXIMANTS USING FOR SOLUTION OF integral equations

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Applied Mathematics and Mechanics(English Edition) 2003年第2期24卷 221-229页

作者：李春景顾传青 DepartmentofMathematics

Two efficient recursive algorithms epsilon_algorithm and eta_algorithm are introduced to compute the generalized inverse function_valued Padé approximants. The approximants were used to accelerate the convergence of the power series with function_valued coefficients and to estimate characteristic value of the integral equations. Famous Wynn identities of the Pad approximants is also established by means of the connection of two algorithms.

关键词： generalized inverse function_valued Padé approximant epsilon_algorithm eta_algorithm integral equations

Accuracy Enhancement Using Spectral Postprocessing for Differential equations and integral equations

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Communications in Computational Physics 2009年第2期5卷 779-792页

作者： Tao Tang Xiang Xu Department of Mathematics Hong Kong Baptist UniversityKowloon TongHong Kong School of Mathematics Fudan UniversityShanghai 200433China.

It is demonstrated that spectral methods can be used to improve the accuracy of numerical solutions obtained by some lower order *** precisely,we can use spectral methods to postprocess numerical solutions of initial value differential *** a few number of iterations(say 3 to 4),the errors can decrease to a few orders of magnitude *** iteration uses the Gauss-Seidel type strategy,which gives an explicit way of *** examples for ODEs,Hamiltonian system and integral equations are *** all indicate that the spectral processing technique can be a very useful way in improving the accuracy of the numerical *** particular,for a Hamiltonian system accuracy is only one of the issues;some other conservative properties are even more important for large time *** spectral postprocessing with the coarse-mesh symplectic initial guess can not only produce high accurate approximations but can also save a significant amount of computational time over the standard symplectic schemes.

关键词： Postprocessing spectral methods rate of convergence Hamiltonian system integral equations

Uniqueness of the Fredholm-Stiltjes Linear integral equations Solutions of the Third Kind

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Advances in Linear Algebra & Matrix Theory 2021年第4期11卷 109-116页

作者： Aizat Toigonbaeva Avyt Asanov Aisalkyn Kambarova Gumushai Obodoeva Ularbek Moldoyarov Aibek Toktorbaev Aichurok Abdukadyr Kyzy Zhypargul Abdullaeva Department of Mathematical Analysis Osh State University Osh Kyrgyzstan Mathematics Department Kyrgyz Turkish Manas University Bishkek Kyrgyzstan Department of Automated Systems and Digital Technologies Osh State University Osh Kyrgyzstan Department of Information Systems and Programming Osh State University Osh Kyrgyzstan Science and Research Department Osh State University Osh Kyrgyzstan

integral equations theoretical parts and applications have been studied and investigated in previous works. In this work, results on investigations of the uniqueness of the Fredholm-Stiltjes linear integral equations solutions of the third kind were considered. Volterra integral equations of the first and third kind with smooth kernels were studied, and proof of the existence of a multiparameter family of solutions is described. Additionally, linear Fredholm integral equations of the first kind were investigated, for which Lavrent’ev regularizing operators were constructed.

关键词： Solution integral equations Uniqueness Fredholm-Stiltjes Linear integral equations Third Kind

MULTIPLE POSITIVE SOLUTIONS TO A SYSTEM OF NONLINEAR HAMMERSTEIN TYPE integral equations

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Annals of Differential equations 2009年第1期25卷 62-66页

作者： Wang Feng, Zhang Fang (School of Math. and Physics, Jiangsu Polytechnic University, Changzhou 213164, Jiangsu) Liu Chunhan (Dept. of Math., Shandong Education College, Jinan 250013) School of Math. and Physics Jiangsu Polytechnic University Changzhou 213164 Jiangsu Dept. of Math. Shandong Education College Jinan 250013

In this paper, we use cone theory and a new method of computation of fixed point index to study a system of nonlinear Hammerstein type integral equations, and the existence of multiple positive solutions to the system... 详细信息

关键词： fixed point index integral equations positive solution