Smoothing transformation and piecewise polynomial collocation for Volterra integro-differential equations with weakly singular kernels

MAREK KOLK; ARVET PEDAS

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Smoothing transformation and piecewise polynomial collocation for Volterra integro-differential equations with weakly singular kernels

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

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The numerical solution of linear weakly singular Volterra integro-differential equations is studied. Using an integral equation reformulation of the initial value problem, we apply to it a smoothing transformation so that the exact solution of the resulting equation does not contain any singularities in its derivatives up to a certain order. After that the regularized equation is solved by a piecewise polynomial collocation method on a mildly graded or uniform grid. Global convergence estimates are derived and some superconvergence results are given.

机译：研究了线性弱奇异Volterra积分微分方程的数值解。使用初始值问题的积分方程式重新公式化，我们对其应用了平滑变换，以使所得方程式的精确解在其导数中直至某个阶数都不含任何奇点。之后，通过分段多项式搭配方法在轻度渐变或均匀网格上求解正则方程。得出全局收敛估计，并给出一些超收敛结果。

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《WSEAS Transactions on Mathematics》 |2007年第4期|共8页
作者
MAREK KOLK; ARVET PEDAS;
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正文语种 eng
中图分类数学;
关键词
Weakly singular Volterra integro-differential equation; Smoothing; Collocation method;

机译：弱奇异Volterra积分微分方程;平滑;配置法;

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专利

1. 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
2. Smoothing Transformation and Piecewise Polynomial Collocation for Weakly Singular Volterra Integral Equations [J] . A. Pedas, G. Vainikko Computing . 2004,第3期

机译：弱奇异Volterra积分方程的平滑变换和分段多项式配置。
3. Piecewise polynomial collocation for fredholm integro-differential equations with weakly singular kernels [J] . Parts I, Pedas A, Tamme E SIAM Journal on Numerical Analysis . 2005,第5期

机译：具有弱奇异核的Fredholm积分-微分方程的分段多项式配置
4. NUMERICAL SOLUTION OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH WEAKLY SINGULAR KERNELS [C] . Sheo Kumar, Harsh Kumar Verma International Conference on Scientific Computing . 2007

机译：弱奇异内核Volterra积分微分方程的数值解
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. A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor Network and Internet of Things [O] . Rohul Amin, Shah Nazir, Iván García-Magariño 2020

机译：无线传感器网络与物联网非线性时滞积分微分方程数值解的配置方法
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. 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

Smoothing transformation and piecewise polynomial collocation for Volterra integro-differential equations with weakly singular kernels

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