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USING FREDHOLM INTEGRAL EQUATION OF THE SECOND KINDTO SOLVE THE VERTICAL VIBRATION OF ELASTICPLATE ON AN ELASTIC HALF SPACE
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作者 金波 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1998年第2期157-162,共6页
The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundary-value condition. By a... The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundary-value condition. By applying Abel transformation the dual integral equations are reduced to Fredholm integral equation of the second kind which is solved numerically. 展开更多
关键词 elastic half space elastic plate dynamic response fredholm integral equation of the second kind
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The Successive Approximation Method for Solving Nonlinear Fredholm Integral Equation of the Second Kind Using Maple
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作者 Dalal Adnan Maturi 《Advances in Pure Mathematics》 2019年第10期832-843,共12页
In this paper, we will use the successive approximation method for solving Fredholm integral equation of the second kind using Maple18. By means of this method, an algorithm is successfully established for solving the... In this paper, we will use the successive approximation method for solving Fredholm integral equation of the second kind using Maple18. By means of this method, an algorithm is successfully established for solving the non-linear Fredholm integral equation of the second kind. Finally, several examples are presented to illustrate the application of the algorithm and results appear that this method is very effective and convenient to solve these equations. 展开更多
关键词 NONLINEAR fredholm INTEGRAL equation of the second kind Successive Approximation Method Maple18
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Function-valued partial Padé-type approximation method for estimating eigenvalues of Fredholm integral equation of the second kind
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作者 顾传青 沈进东 《Journal of Shanghai University(English Edition)》 CAS 2007年第6期531-535,共5页
Abstract A new function-valued partial Padé-type approximation was introduced in the polynomial space, and an explicit determinant formula was derived by means of some orthogonal polynomials. This method can be a... Abstract A new function-valued partial Padé-type approximation was introduced in the polynomial space, and an explicit determinant formula was derived by means of some orthogonal polynomials. This method can be applied to estimating surplus eigenvalues of the Fredholm integral equation of the second kind when its partial eigenvalues have been known, and at the same time, it can be applied to solving the approximating solution of the given equation. 展开更多
关键词 linear functional function-valued partial Padé approximation DETERMINANT fredholm integral equation of thesecond kind eigenvalue.
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A Method for Solving Fredholm Integral Equations of the First Kind Based on Chebyshev Wavelets 被引量:2
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作者 M. Bahmanpour M. A.Fariborzi Araghi 《Analysis in Theory and Applications》 2013年第3期197-207,共11页
In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] a... In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other. 展开更多
关键词 First kind fredholm integral equation Galerkin and Modified Galerkin method Legendre wavelets Chebyshev wavelets.
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ON THE REGULARIZATION METHOD OF THE FIRST KIND OFFREDHOLM INTEGRAL EQUATION WITH A COMPLEX KERNEL AND ITS APPLICATION
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作者 尤云祥 缪国平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1998年第1期75-83,共9页
The regularized integrodifferential equation for the first kind of Fredholm, integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate reg... The regularized integrodifferential equation for the first kind of Fredholm, integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate regularized solutions is discussed. As an application of the method, an inverse problem in the two-dimensional wave-making problem of a flat plate is solved numerically, and a practical approach of choosing optimal regularization parameter is given. 展开更多
关键词 inverse problem fredholm integral equation of the first kind complex kernel regularization method
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Uniqueness of the Fredholm-Stiltjes Linear Integral Equations Solutions of the Third Kind
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作者 Aizat Toigonbaeva Avyt Asanov +5 位作者 Aisalkyn Kambarova Gumushai Obodoeva Ularbek Moldoyarov Aibek Toktorbaev Aichurok Abdukadyr Kyzy Zhypargul Abdullaeva 《Advances in Linear Algebra & Matrix Theory》 2021年第4期109-116,共8页
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 ... 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. 展开更多
关键词 Solution Integral equations UNIQUENESS fredholm-Stiltjes Linear Integral equations Third kind
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Numerical Algorithms for Solving One Type of Singular Integro-Differential Equation Containing Derivatives of the Time Delay States 被引量:1
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作者 Shihchung Chiang Terry L. Herdman 《Applied Mathematics》 2015年第8期1294-1301,共8页
This study presents numerical algorithms for solving a class of equations that partly consists of derivatives of the unknown state at previous certain times, as well as an integro-differential term containing a weakly... This study presents numerical algorithms for solving a class of equations that partly consists of derivatives of the unknown state at previous certain times, as well as an integro-differential term containing a weakly singular kernel. These equations are types of integro-differential equation of the second kind and were originally obtained from an aeroelasticity problem. One of the main contributions of this study is to propose numerical algorithms that do not involve transforming the original equation into the corresponding Volterra equation, but still enable the numerical solution of the original equation to be determined. The feasibility of the proposed numerical algorithm is demonstrated by applying examples in measuring the maximum errors with exact solutions at every computed nodes and calculating the corresponding numerical rates of convergence thereafter. 展开更多
关键词 Integro-Differential equation of the second kind WEAKLY SINGULAR KERNEL Numerical Algorithms Rates of Convergence
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New Complex Solutions of the Coupled KdV Equations
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作者 FAN Jun-jie LI Guang-fang Taogetusang 《Chinese Quarterly Journal of Mathematics》 2021年第1期41-48,共8页
In this paper,new infinite sequence complex solutions of the coupled Kd V equations are constructed with the help of function transformation and the second kind of elliptic equation.First of all,according to the funct... In this paper,new infinite sequence complex solutions of the coupled Kd V equations are constructed with the help of function transformation and the second kind of elliptic equation.First of all,according to the function transformation,the coupled Kd V equations are changed into the second kind of elliptic equation.Secondly,the new solutions and Bäcklund transformation of the second kind of elliptic equation are applied to search for new infinite sequence complex solutions of the coupled Kd V equations.These solutions include new infinite sequence complex solutions composed by Jacobi elliptic function,hyperbolic function and triangular function. 展开更多
关键词 the coupled KdV equations Function transformation the second kind of elliptic equation Complex solutions
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第二类Fredholm模糊积分方程的模糊数值解
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作者 刘雪铃 黄静 +1 位作者 冯依虎 崔钰晗 《滨州学院学报》 2024年第2期46-51,共6页
研究了一类模糊集意义下的第二类Fredholm模糊积分方程的数值解。采用残余幂级数法得到第二类Fredholm模糊积分方程的k级截断级数解,将第二类Fredholm模糊积分方程的数值解用泰勒光滑公式展开,并通过代数方程组求解出相关系数。最后,结... 研究了一类模糊集意义下的第二类Fredholm模糊积分方程的数值解。采用残余幂级数法得到第二类Fredholm模糊积分方程的k级截断级数解,将第二类Fredholm模糊积分方程的数值解用泰勒光滑公式展开,并通过代数方程组求解出相关系数。最后,结合数值算例证明了残余幂级数方法的稳定性和收敛性。 展开更多
关键词 第二类fredholm模糊积分方程 残余幂级数法 模糊微分方程 数值解 模糊函数
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Infinite Sequence Soliton-Like Exact Solutions of (2 + 1)-Dimensional Breaking Soliton Equation 被引量:19
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作者 Taogetusang Sirendaoerji 李姝敏 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第6期949-954,共6页
To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations (NEE(s)), by developing two characteristics of construction and mechanization on auxiliary equation method, the second ki... To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations (NEE(s)), by developing two characteristics of construction and mechanization on auxiliary equation method, the second kind of elliptie equation is highly studied and new type solutions and Backlund transformation are obtained. Then (2+ l )-dimensional breaking soliton equation is chosen as an example and its infinite sequence soliton-like exact solutions are constructed with the help of symbolic computation system Mathematica, which include infinite sequence smooth soliton-like solutions of Jacobi elliptic type, infinite sequence compact soliton solutions of Jacobi elliptic type and infinite sequence peak soliton solutions of exponential function type and triangular function type. 展开更多
关键词 the second kind of elliptic equation Backlund transformation nonlinear evolution equation infi-nite sequence soliton-like exact solution
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Theoretical and Experimental Studies of the Effect of Inclined Scraper on Removal of Raw Cotton from Mesh Surface 被引量:3
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作者 Muradov Rustam Muradovich Karimov Abdusamat Ismonovich Mardanov Botir Mardanovich 《World Journal of Mechanics》 2014年第12期371-377,共7页
The present manuscript deals with theoretical and experimental studies of the effect of inclined scraper on removal raw cotton from mesh surface. The mathematical model of the problem and theoretical studies of the mo... The present manuscript deals with theoretical and experimental studies of the effect of inclined scraper on removal raw cotton from mesh surface. The mathematical model of the problem and theoretical studies of the motion of cotton mass on plane of scraper is derived taking into account material point by accomplishing plane motion in the mesh surface. Graphs of the experiment shows that performance of scraper inclined to the radius of the disk by the value α=30° to the surface mesh β=110°, optimally allows to reduce the formation of technological defects of raw cotton. The presence of zero-pressure portion on the mesh surface of separator may provide complete removal of cotton from its surface and to eliminate grid clogging. 展开更多
关键词 Cotton AIR SCRAPER SHAFT SEPARATOR Radial and ANGULAR AIR Speed LAGRANGE equations of the second kind Trajectory
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基于半正交B样条小波的第二类分数阶Fredholm积分方程数值解法
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作者 闫洁 韩惠丽 +1 位作者 周春梅 白龙 《西北师范大学学报(自然科学版)》 CAS 北大核心 2023年第2期12-17,共6页
采用半正交B样条小波方法将第二类线性分数阶Fredholm积分方程的核函数、已知函数和未知函数展开,给出收敛性定理及误差分析;结合选取的等距配置点将积分方程转化为线性代数方程组进行求解;通过数值算例验证了方法的有效性.
关键词 第二类fredholm积分方程 半正交B样条小波 分数阶微积分 配置法
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Fast Solvers of Fredholm Optimal Control Problems
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作者 Mario Annunziato Alfio Borzi 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2010年第4期431-448,共18页
The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of ... The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments. 展开更多
关键词 Optimal control theory fredholm integral equations of second kind iterative methods
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PRECONDITIONED CONJUGATE GRADIENT METHODS FOR INTEGRAL EQUATIONS OF THE SECOND KIND DEFINED ON THE HALF-LINE
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作者 Chan, RH Lin, FR 《Journal of Computational Mathematics》 SCIE CSCD 1996年第3期223-236,共14页
We consider solving integral equations of the second kind defined on the half-line [0, infinity) by the preconditioned conjugate gradient method. Convergence is known to be slow due to the non-compactness of the assoc... We consider solving integral equations of the second kind defined on the half-line [0, infinity) by the preconditioned conjugate gradient method. Convergence is known to be slow due to the non-compactness of the associated integral operator. In this paper, we construct two different circulant integral operators to be used as preconditioners for the method to speed up its convergence rate. We prove that if the given integral operator is close to a convolution-type integral operator, then the preconditioned systems will have spectrum clustered around 1 and hence the preconditioned conjugate gradient method will converge superlinearly. Numerical examples are given to illustrate the fast convergence. 展开更多
关键词 MATH Cr PRECONDITIONED CONJUGATE GRADIENT METHODS FOR INTEGRAL equationS of the second kind DEFINED ON the HALF-LINE PRO III
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基于有理Haar小波求解分数阶第2类Fredholm积分方程 被引量:5
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作者 张倩 韩惠丽 张盼盼 《江西师范大学学报(自然科学版)》 CAS 北大核心 2014年第1期47-50,82,共5页
利用有理Haar小波函数数值求解分数阶第2类Fredholm积分方程,用有理Haar小波定义及性质与配置法给出有理Haar小波积分算子矩阵,将积分方程转化为代数方程组进行求解.最后通过误差分析和数值算例将分数阶积分方程的精确解和用Haar小波所... 利用有理Haar小波函数数值求解分数阶第2类Fredholm积分方程,用有理Haar小波定义及性质与配置法给出有理Haar小波积分算子矩阵,将积分方程转化为代数方程组进行求解.最后通过误差分析和数值算例将分数阶积分方程的精确解和用Haar小波所得数值解进行比较,表明了该算法具有较高的精确度. 展开更多
关键词 有理Haar小波 分数阶 第2类fredholm积分方程 配置法
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用第二类Fredholm积分方程求解弹性半空间上弹性板的垂直振动 被引量:6
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作者 金波 《应用数学和力学》 EI CSCD 北大核心 1998年第2期145-150,共6页
根据混合边值条件,建立均布简谐荷载作用下弹性半空间上弹性板振动的对偶积分方程·用Abel变换化对偶积分方程为第二类Fredholm积分方程,并进行了数值计算·
关键词 弹性半空间 弹性板 动力响应 积分方程 垂直振动
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ASYMPTOTIC ERROR EXPANSION FOR THE NYSTROM METHOD OF NONLINEAR VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND
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作者 Han Guo-qiang (Dept. Of Comp, Science, South China University of Science and Technology, Guangzhou, China) 《Journal of Computational Mathematics》 SCIE CSCD 1994年第1期31-35,共5页
While the numerical solution of one-dimensional Volterra integral equations of the second kind with regular kernels is well understood, there exist no systematic studies of asymptotic error expansion for the approxima... While the numerical solution of one-dimensional Volterra integral equations of the second kind with regular kernels is well understood, there exist no systematic studies of asymptotic error expansion for the approximate solution. In this paper,we analyse the Nystrom solution of one-dimensional nonlinear Volterra integral equation of the second kind and show that approkimate solution admits an asymptotic error expansion in even powers of the step-size h, beginning with a term in h2. So that the Richardson's extrapolation can be done. This will increase the accuracy of numerical solution greatly. 展开更多
关键词 ASYMPTOTIC ERROR EXPANSION FOR the NYSTROM METHOD of NONLINEAR VOLTERRA INTEGRAL equation of the second kind
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第二类勒让德函数的重规格化及其优化
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作者 张捍卫 杨永勤 +1 位作者 李晓玲 张华 《测绘学报》 EI CSCD 北大核心 2024年第7期1298-1307,共10页
椭球谐函数级数展开是地球重力场椭球谐建模的基础。然而,处理椭球谐函数级数的主要困难在于计算第二类勒让德函数。而Jekeli的重规格化方法简化了这一计算过程。本文在Jekeli重规格化的基础上,详细推导了两种基于高斯超几何函数变换的... 椭球谐函数级数展开是地球重力场椭球谐建模的基础。然而,处理椭球谐函数级数的主要困难在于计算第二类勒让德函数。而Jekeli的重规格化方法简化了这一计算过程。本文在Jekeli重规格化的基础上,详细推导了两种基于高斯超几何函数变换的优化递归方法,同时利用这两种优化递归的方法计算了第二类勒让德函数,并将其展开到二阶导数。通过数值计算,证明了优化递归方法可以有效加快收敛,缩短计算时间,并且适用阶数更高,这使得椭球谐函数级数在实际应用中更加方便、可行。 展开更多
关键词 第二类勒让德函数 缔合勒让德微分方程 重规格化 高斯超几何函数
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L^2(R^p)框架与第二类Fredholm积分方程的解析解 被引量:1
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作者 施云惠 吴勃英 《哈尔滨工业大学学报》 EI CAS CSCD 北大核心 2000年第6期125-127,131,共4页
构造了多元小波框架以及多元函数小波框架展开式 。
关键词 第二类 fredholm积分方程 多元小波框架 多元函数 解析解
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第一类Fredholm积分方程的解析解 被引量:2
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作者 施云惠 王子才 《黑龙江大学自然科学学报》 CAS 2000年第1期16-18,21,共4页
构造了多元小波框架以及多元函数小波框架展开公式,进而给出了第一类 fredholm积分 方程的解析解。
关键词 小波 多元函数逼近 fredholm积分方程 解析解
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