ON THE REGULARIZATION METHOD OF THE FIRST KIND OFFREDHOLM INTEGRAL EQUATION WITH A COMPLEX KERNEL AND ITS APPLICATION

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.

A Method for Solving Fredholm Integral Equations of the First Kind Based on Chebyshev Wavelets

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.

Function-valued partial Padé-type approximation method for estimating eigenvalues of Fredholm integral equation of the second kind

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.

USING FREDHOLM INTEGRAL EQUATION OF THE SECOND KINDTO SOLVE THE VERTICAL VIBRATION OF ELASTICPLATE ON AN ELASTIC HALF SPACE

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.

The Successive Approximation Method for Solving Nonlinear Fredholm Integral Equation of the Second Kind Using Maple

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.

Uniqueness of the Fredholm-Stiltjes Linear Integral Equations Solutions of the Third Kind

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.

第二类Fredholm模糊积分方程的模糊数值解

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。

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

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.

A Jacobi-collocation method for solving second kind Fredholm integral equations with weakly singular kernels

In this work,we propose a Jacobi-collocation method to solve the second kind linear Fredholm integral equations with weakly singular kernels.Particularly,we consider the case when the underlying solutions are sufficiently smooth.In this case,the proposed method leads to a fully discrete linear system.We show that the fully discrete integral operator is stable in both infinite and weighted square norms.Furthermore,we establish that the approximate solution arrives at an optimal convergence order under the two norms.Finally,we give some numerical examples,which confirm the theoretical prediction of the exponential rate of convergence.

解第一类Fredholm积分方程的优化正则化策略

探讨了第一类Fredholm积分方程的病态性及其正则化求解策略的构建问题 ,并建立了一种改进的Tikhonov正则化算法 .通过适当选取正则参数 。

第一类Fredholm积分方程的解析解

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。

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

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·

一种新的求解第一类Fredholm积分方程正则化的数值分析

应用改进的Tikhonov正则化 ,借助Matlab软件对一类Fredholm积分方程进行数值求解 .结果表明 ,李功胜等所建立的改进的Tikhonov正则化比通常的Tikhonov正则化更精确 ,而且正则解能够达到与理论分析基本一致的较高的收敛率 .

L^2(R^p)框架与第二类Fredholm积分方程的解析解

构造了多元小波框架以及多元函数小波框架展开式 。

求解第一类Fredholm积分方程的小波-正则化方法及外推

利用Legendre小波Galerkin方法将积分方程转化为线性方程组,对n+1个不同的正则化子分别利用Tikhonov正则化方法求解,得到了n+1组不同的稳定解。然后应用Newton插值公式求得了正则化子为零时积分方程的最佳稳定解。数值算例表明,方法是非常有效的。

Fredholm第一类积分方程数值解的可靠性

讨论了一个Ｆｒｅｄｈｏｌｍ第一类积分方程数值解的可靠性问题．对于Ｆａｂｒｙ－Ｐｅｒｏｔ干涉反演光谱学中的第一类积分方程，当Δσ＝２／ｘ，Δｘ＝２／σ，且等距取样点数为一个适当的奇数时，虽然采用最简单的矩形求积公式可离散得一个稳定的线性方程组，但是该方程组的解却不是原积分方程的解，换句话说，该稳定的数值解是不可靠的．

第二类Fredholm积分方程的数值解法

首先介绍了第二类 Fredholm 积分方程,然后设计求解第二类 Fredhlom 积分方程的数值格式,即利用 Simpson公式或 Gauss 型求积公式进行数值积分,寻找近似解 u(x).算例结果表明,该数值解法具有高精度性质.

二维第二类Fredholm方程有限元解的迭代校正

对二维第二类Fredholm积分方程，以有限元解为基础，建立了一个高精度算法——迭代校正法。证明了在光滑核条件下，对双线性有限元解进行一次迭代校正，可使精度从O（h2）提高到O（h6）。

Karhunen-Loeve展开在Abaqus中的实现

基于数值分析理论,提出一种Karhunen-Loeve展开的数值算法,采用Python和Fortran混合编码的方式将其内嵌至Abaqus的计算内核中,分析程序编制的关键要素并开展误差分析。结果表明:编制的程序可行,随机场展开合理,数值算法精度较高,特征值、特征函数以及协方差函数的计算结果与理论解一致。

带复数核的第一类Fredholm积分方程的正则化方法及其应用

本文推广了Ｔｉｋｈｏｎｏｖ正则化方法，导出了带复数核的第一类Ｆｒｅｄｈｏｌｍ积分方程的正则解应满足的正则积分微分方程，并讨论了正则解的收敛性·作为这一方法的应用，数值求解了与二维摇板造波问题相应的一类逆问题。