The piecewise polynomial collocation method for nonlinear weakly singular volterra equations

Hermann Brunner; Arvet Pedas; Gennadi Vainikko

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The piecewise polynomial collocation method for nonlinear weakly singular volterra equations

机译：非线性弱奇异Volterra方程的分段多项式配置方法

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摘要

Second-kind volterra integral equations with weakly singular kernels typically have solutions which are nonsmooth near the initial point of the interval of integration. Using an adaptation of the analysis originally developed for nonlinear weakly singular Fredholm integral equations, we present a complete discussion of the optimal (global and local) order of convergence of piecewise polynomial collocation methods on graded grids for nonlinear Volterra integral equations with algebraic or logarithmic singularities in their kernels.

机译：具有弱奇异核的第二类Volterra积分方程通常具有在积分间隔的起始点附近不平滑的解决方案。使用最初针对非线性弱奇异Fredholm积分方程开发的分析的调整，我们对带代数或对数奇异非线性非线性Volterra积分方程的分段网格上分段多项式搭配方法的最优（全局和局部）收敛阶次进行了完整的讨论在他们的内核中。

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《Mathematics of computation》 |1999年第227期|共17页
作者
Hermann Brunner; Arvet Pedas; Gennadi Vainikko;
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正文语种 eng
中图分类数学;
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nonlinear weakly singular volterra and fredholm integral equations; piecewise polynomial collocation; graded grids; optimal order of convergence;

机译：非线性弱奇异Volterra和Fredholm积分方程;分段多项式配置;渐变网格;收敛的最优阶;

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1. 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
2. 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
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. The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations [O] . Hermann Brunner, Arvet Pedas, Gennadi Vainikko 1999

机译：非线性弱奇异Volterra方程的分段多项式搭配方法
8. Piecewise Polynomial Collocation Methods for Linear Volterra Integro-DifferentialEquations with Weakly Singular Kernels [R] . Brunner, H., Pedas, A., Vainikko, G. 2000

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

The piecewise polynomial collocation method for nonlinear weakly singular volterra equations

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