DISCRETE SUPERCONVERGENCE OF COLLOCATION SOLUTIONS FOR FIRST-KIND VOLTERRA INTEGRAL EQUATIONS

HUI LIANG; HERMANN BRUNNER

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DISCRETE SUPERCONVERGENCE OF COLLOCATION SOLUTIONS FOR FIRST-KIND VOLTERRA INTEGRAL EQUATIONS

机译：一类Volterra积分方程的解的离散超收敛

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It is known that collocation solutions for first-kind Volterra integral equations based on (discontinuous or continuous) piecewise polynomials cannot exhibit local super-convergence at the points of a uniform mesh. In this paper we present a complete analysis of local superconvergence of such collocation solutions for first-kind Volterra integral equations at non-mesh points. In particular, we discuss (i) the existence of superconvergence points for prescribed collocation points; (ii) the existence of collocation points for prescribed super-convergence points. Numerous examples illustrate the theory.

机译：众所周知，基于（不连续或连续）分段多项式的第一类Volterra积分方程的搭配解不能在均匀网格的点处表现出局部超收敛性。在本文中，我们对非网格点上第一类Volterra积分方程的此类配点解的局部超收敛进行了完整的分析。特别是，我们讨论（i）规定搭配点的超收敛点的存在; （ii）规定的超收敛点的并置点的存在。大量的例子说明了这一理论。

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《The Journal of integral equations and applications》 |2012年第3期|共33页
作者
HUI LIANG; HERMANN BRUNNER;
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正文语种 eng
中图分类数学;
关键词
First-kind Volterra integral equations; collocation solutions; piecewise polynomials; superconvergence at non-mesh points.;

机译：一类Volterra积分方程;配置解;分段多项式;非网格点的超收敛;

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1. DISCRETE SUPERCONVERGENCE OF COLLOCATION SOLUTIONS FOR FIRST-KIND VOLTERRA INTEGRAL EQUATIONS [J] . HUI LIANG, HERMANN BRUNNER The Journal of integral equations and applications . 2012,第3期

机译：一类Volterra积分方程的解的离散超收敛
2. Optimal superconvergence orders of iterated collocation solutions for volterra integral equations with vanishing delays [J] . Brunner H, Hu QY SIAM Journal on Numerical Analysis . 2005,第5期

机译：具有消失的Volterra积分方程的迭代配置解的最优超收敛阶
3. On global superconvergence of iterated collocation solutions to linear second-kind Volterra integral equations [J] . Hermann Brunner, Ningning Yan Journal of Computational and Applied Mathematics . 1996,第1期

机译：线性第二类Volterra积分方程的迭代配点解的全局超收敛
4. Numerical solution of a singular Volterra integral equation by piecewise polynomial collocation [C] . T. Diogo, S. Valtchev, P. Lima Ninth International Conference on Enhancement and Promotion of Computational Methods in Engineering and Science (EPMESC IX); Nov 25-28, 2003; Macao, China . 2003

机译：分段多项式配置的奇异Volterra积分方程的数值解
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. Jacobi spectral collocation method for the approximate solution of multidimensional nonlinear Volterra integral equation [O] . Yunxia Wei, Yanping Chen, Xiulian Shi, -1

机译：多维非线性Volterra积分方程近似解的Jacobi谱配点法
7. Superconvergence of interpolated collocation solutions for weakly singular Volterra integral equations of the second kind [O] . Qiumei Huang, Min Wang 2021

机译：第二种弱奇异Volterra积分方程的内插搭配解决方案的超级度验证
8. Superconvergence in Collocation and Implicit Runge-Katta Methods for Volterra-Type Integral Equations of the Second Kind [R] . Brunner, H. 1980

机译：第二类Volterra型积分方程的配置和隐式Runge-Katta方法的超收敛性

DISCRETE SUPERCONVERGENCE OF COLLOCATION SOLUTIONS FOR FIRST-KIND VOLTERRA INTEGRAL EQUATIONS

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