Cubic spline collocation for a class of weakly singular Fredholm integral equations and corresponding eigenvalue problem

机译：一类弱奇异Fredholm积分方程的三次样条搭配及相应的特征值问题

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The numerical solution of a class of linear Fredholm integral equations of the second kind and corresponding eigenvalue problem by the collocation method is discussed. The kernel of the integral equation may have weak diagonal and boundary singularities. Using C~2-smooth cubic splines and special non-uniform grids, the convergence rate of proposed numerical schemes is studied.

机译：讨论了一类第二类线性弗雷德霍尔姆积分方程的数值解以及相应的特征值问题。积分方程的核可能具有弱的对角线和边界奇点。利用C〜2光滑三次样条和特殊的非均匀网格，研究了所提出数值方案的收敛速度。

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来源
《Mathematical methods for information science and economics》|2012年|127-132|共6页
会议地点 Montreux(CH)
作者
ARVET PEDAS; MIKK VIKERPUUR;
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作者单位

Institute of Mathematics University of Tartu J. Liivi 2, 50409 Tartu ESTONIA;

Institute of Mathematics University of Tartu J. Liivi 2, 50409 Tartu ESTONIA;

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正文语种 eng
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关键词
Weakly singular integral equation; boundary singularity; cubic spline collocation method; graded grid; eigenvalue problem;

机译：弱奇异积分方程；边界奇点三次样条搭配法；渐变网格；特征值问题;

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专利

1. QUADRATIC SPLINE COLLOCATION FOR THE SMOOTHED WEAKLY SINGULAR FREDHOLM INTEGRAL EQUATIONS [J] . Rene Pallav, Arvet Pedas Numerical Functional Analysis and Optimization . 2009,第9a10期

机译：光滑的弱奇异Fredholm积分方程的二次样条插值
2. Error analysis of Jacobi spectral collocation methods for Fredholm-Hammerstein integral equations with weakly singular kernel [J] . Panigrahi Bijaya Laxmi International journal of computer mathematics . 2019,第5a8期

机译：具有弱奇异核的Fredholm-Hammerstein积分方程Jacobi谱配点方法的误差分析
3. Error analysis of Jacobi spectral collocation methods for Fredholm-Hammerstein integral equations with weakly singular kernel [J] . Panigrahi Bijaya Laxmi International journal of computer mathematics . 2019,第5a8期

机译：弗雷霍尔姆 - Hammerstein整体方程与弱奇异内核的误差分析
4. Cubic spline collocation for a class of weakly singular Fredholm integral equations and corresponding eigenvalue problem [C] . ARVET PEDAS, MIKK VIKERPUUR WSEAS International Conference on Applied Mathematics . 2013

机译：一类弱奇异的Fredholm整体方程的立方样条搭配和相应的特征值问题
5. CONVERGENCE AND SUPERCONVERGENCE OF NUMERICAL SOLUTIONS OF WEAKLY SINGULAR INTEGRAL AND DIFFERENTIAL EQUATIONS (GALERKIN, COLLOCATION, EIGENVALUES, EIGENVECTORS, SPLINES) [D] . LEBBAR, RACHID. 1986

机译：弱奇异积分和微分方程数值解的收敛性和超级度验收（Galerkin，Collocation，特征值，特征向量，花键）
6. A NEW APPROACH TO THE NUMERICAL SOLUTION OF A CLASS OF LINEAR AND NONLINEAR INTEGRAL EQUATIONS OF FREDHOLM TYPE [O] . Richard Bellman 1965

机译：一类Fredholm型线性和非线性积分方程数值解的新方法。
7. Sinc-collocation methods for weakly singular Fredholm integral equations of the second kind [O] . Okayama Tomoaki, Matsuo Takayasu, Sugihara Masaaki 2010

机译：第二类弱奇异Fredholm积分方程的Sinc配置方法
8. Spline Collocation Method for Integral Equations of the First Kind with Logarithmic Singularity [R] . Guseinov, E. A., Hermans, A. J. 1987

机译：具有对数奇异性的第一类积分方程的样条配置法

Cubic spline collocation for a class of weakly singular Fredholm integral equations and corresponding eigenvalue problem

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