Sinc collocation approximation of non-smooth solution of a nonlinear weakly singular Volterra integral equation

Zakeri G.-A.; Navab M.

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Sinc collocation approximation of non-smooth solution of a nonlinear weakly singular Volterra integral equation

机译：非线性弱奇异Volterra积分方程非光滑解的Sinc配置近似

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摘要

A numerical method based on sinc collocation approximation for a class of nonlinear weakly singular Volterra integral equations of a second kind with non-smooth solution is given. The numerical method given here combines a sinc collocation method with an explicit iterative process that involves solving a nonlinear system of equations. We provide an error analysis for the method. It is shown that the approximate solution converges to the exact solution at the rate of Mexp(-cM), where M is the number of collocation points and c is some positive constant. Some numerical results for several test functions are given to confirm the accuracy and the ease of implementation of the method.

机译：给出了一种基于sinc配置近似的第二类非线性非奇异Volterra积分方程的非光滑解的数值方法。此处给出的数值方法将Sinc配置方法与显式迭代过程结合在一起，该过程涉及求解非线性方程组。我们提供了该方法的错误分析。结果表明，近似解以Mexp（-cM）的速率收敛到精确解，其中M为配置点的数量，c为某个正常数。给出了几个测试函数的一些数值结果，以确认该方法的准确性和易实现性。

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《Journal of Computational Physics》 |2010年第18期|共10页
作者
Zakeri G.-A.; Navab M.;
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正文语种 eng
中图分类数学物理方法;
关键词
Nonlinear singular Volterra integral equation of second kind; Sinc collocation method; Weakly singular kernel; Whittaker's cardinal function;

机译：第二类非线性奇异Volterra积分方程;Sinc配点法;弱奇异核;Whittaker基数函数;

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1. Sinc collocation approximation of non-smooth solution of a nonlinear weakly singular Volterra integral equation [J] . Zakeri G.-A., Navab M. Journal of Computational Physics . 2010,第18期

机译：非线性弱奇异Volterra积分方程非光滑解的Sinc配置近似
2. A polynomial collocation method for the numerical solution of weakly singular and singular integral equations on non-smooth boundaries [J] . G. Monegato, L. Scuderi International Journal for Numerical Methods in Engineering . 2003,第13期

机译：非光滑边界上的弱奇异和奇异积分方程数值解的多项式配置方法
3. Convergence analysis of Sinc-collocation methods for nonlinear Fredholm integral equations with a weakly singular kernel [J] . Maleknejad K., Mollapourasl R., Ostadi A. Journal of Computational and Applied Mathematics . 2015,第Null期

机译：具有弱奇异核的非线性Fredholm积分方程Sinc-colocation方法的收敛性分析
4. Numerical Solutions of Nonlinear Volterra–Fredholm–Hammerstein Integral Equations Using Sinc Nystr?m Method [C] . Yanying Ma, Jin Huang, Changqing Wang International Conference on Information Technology and Intelligent Transportation Systems . 2017

机译：慈爱NYSTRαM方法的非线性Volterra-Fredholm-Hammerstein整体方程的数值解
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. 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

Sinc collocation approximation of non-smooth solution of a nonlinear weakly singular Volterra integral equation

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