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Volterra Integral Equations of the Second Kind with Nonsmooth Solutions: High-Order Methods Based on Collocation Techniques

机译：具有非光滑解的第二类Volterra积分方程：基于配置技术的高阶方法

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摘要

Methods with arbitrary order of convergence are derived for the approximate solution of second kind Volterra integral equations with weakly singular kernels where exact solutions have unbounded derivatives at the left endpoint of the interval of integration. These methods are based on collocation techniques in certain nonsmooth piecewise function spaces whose elements reflect the singular behavior of the given equation.

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作者
Brunner, H.; Teriele, H. J. J.;
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年度 1982
页码 p.1-23
总页数 23
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Collocation; Differential calculus; Numerical integration; Singularity (Mathematics); Volterra equations; Convergence; Half planes; Kernel functions; Singular integral equations; Uniqueness theorem;

机译：配置;微积分;数值积分;奇异性（数学）; Volterra方程;收敛;半平面;核函数;奇异积分方程;唯一性定理;

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专利

1. Integral Collocation Approximation Methods for the Numerical Solution of High-Orders Linear Fredholm-Volterra Integro-Differential Equations [J] . Abubakar A., Taiwo O. A. American Journal of Computational and Applied Mathematics . 2014,第4期

机译：高阶线性Fredholm-Volterra积分微分方程数值解的积分配置近似方法
2. Numerical solution of Volterra-Fredholm integral equations using the collocation method based on a special form of the Muntz-Legendre polynomials [J] . Negarchi Neda, Nouri Kazem Journal of Computational and Applied Mathematics . 2018,第期

机译：基于Muntz-Legendre多项式的特殊形式的搭配方法使用搭配方法的Volterra-Fredholm积分方程的数值解
3. Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via collocation method based on radial basis functions [J] . Parand K., Rad J.A. Applied mathematics and computation . 2012,第9期

机译：基于径向基函数的搭配法非线性Volterra-Fredholm-Hammerstein积分方程的数值解
4. A Family of Multistep Collocation Methods for Volterra Integral Equations [C] . D. Conte, B. Paternoster International Conference on Numerical Analysis and Applied Mathematics . 2007

机译：Volterra Integral方程的一个多步配置方法
5. Numerical solution of integral equations with nonsmooth kernel and applications. [D] . Kang, Sheon Young. 2000

机译：具有非光滑核的积分方程的数值解及其应用。
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. The Numerical Solution of Nonlinear Volterra Integral Equations of the Second Kind by Collocation and Iterated Collocation Methods [O] . J. G. Blom, H. Brunner 1987

机译：通过搭配和迭代配套方法的第二种非线性Volterra积分方程的数值解
8. Collocation Methods for Weakly Singular Second Kind Volterra Integral Equations with Nonsmooth Solution [R] . Teriele, H. J. J. 1981

机译：具有非光滑解的弱奇异二阶Volterra积分方程的配置方法

Volterra Integral Equations of the Second Kind with Nonsmooth Solutions: High-Order Methods Based on Collocation Techniques

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