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Piecewise Polynomial Collocation Methods for Linear Volterra Integro-DifferentialEquations with Weakly Singular Kernels

机译：具有弱奇异核的线性Volterra积分微分方程的分段多项式配置方法

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摘要

The smoothness of the solution of a linear weakly singular Volterra integro-differential equations is studied. Two piecewise polynomial collocation methods are discussed to solve such equations. Global convergence estimates have been derived and the superconvergence effect at collocation points has been analyzed.

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作者
Brunner, H.; Pedas, A.; Vainikko, G.;
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年度 2000
页码 1-32
总页数 32
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Volterra integral equations; Polynomials; Linear systems; Mathematical models; Kernel functions; Convergence; Cauchy problems;

机译：Volterra积分方程;多项式;线性系统;数学模型;核函数;收敛性; Cauchy问题;

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专利

1. Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels [J] . Brunner H., Vainikko G., Pedas A. SIAM Journal on Numerical Analysis . 2001,第3期

机译：具有弱奇异核的线性Volterra积分微分方程的分段多项式配置方法
2. The piecewise polynomial collocation method for nonlinear weakly singular volterra equations [J] . Hermann Brunner, Arvet Pedas, Gennadi Vainikko Mathematics of computation . 1999,第227期

机译：非线性弱奇异Volterra方程的分段多项式配置方法
3. Smoothing transformation and piecewise polynomial collocation for Volterra integro-differential equations with weakly singular kernels [J] . MAREK KOLK, ARVET PEDAS WSEAS Transactions on Mathematics . 2007,第4期

机译：具有弱奇异核的Volterra积分-微分方程的平滑变换和分段多项式配置
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 in the Maximum Norm of a Class of Piecewise Polynomial Collocation Methods for Solving Linear Weakly Singular Volterra Integro-Differential Equations [O] . Raul Kangro, Inga Parts 2003

机译：用于求解线性弱奇异Volterra积分差分方程的一类分段多项式搭配方法的最大规范
8. Multiquadric collocation methods in the numerical solution of Volterra integral equations with weakly singular kernels [R] . Makroglou, A, Kansa, E J 1993

机译：具有弱奇异核的Volterra积分方程数值解中的多元配置方法

Piecewise Polynomial Collocation Methods for Linear Volterra Integro-DifferentialEquations with Weakly Singular Kernels

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