RBFs for Integral Equations with a Weakly Singular Kernel

Jafar Biazar; Mohammad Ali Asadi

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RBFs for Integral Equations with a Weakly Singular Kernel

机译：具有弱奇异核的积分方程的RBF

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摘要

In this paper a numerical method, based on collocation method and radial basis functions (RBF) is proposed for solving integral equations with a weakly singular kernel. Integrals appeared in the procedure of the solution are approximated by adaptive Lobatto quadrature rule. Illustrative examples are included to demonstrate the validity and applicability of the presented technique. In addition, the results of applying the method are compared with those of Homotopy perturbation, and Adomian decomposition methods.

机译：本文提出了一种基于配置方法和径向基函数（RBF）的数值方法，用于求解具有弱奇异核的积分方程。解的过程中出现的积分通过自适应Lobatto正交规则近似。包括说明性示例以证明所提出技术的有效性和适用性。此外，将该方法的应用结果与同伦摄动和Adomian分解方法的结果进行了比较。

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《American Journal of Applied Mathematics》 |2015年第6期|共6页
作者
Jafar Biazar; Mohammad Ali Asadi;
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1. Variable transformations in the numerical solution of second kind Volterra integral equations with continuous and weakly singular kernels; extensions to Fredholm integral equations [J] . E. A. Galperin, E. J. Kansa, A. Makroglou, Journal of Computational and Applied Mathematics . 2000,第1a2期

机译：具有连续和弱奇异核的第二类Volterra积分方程数值解的变量变换; Fredholm积分方程的扩展
2. FD-RBF for Partial Integro-Differential Equations with a Weakly Singular Kernel [J] . Jafar Biazar, Mohammad Ali Asadi Applied and Computational Mathematics . 2015,第6期

机译：具有弱奇异核的偏微分方程的FD-RBF
3. Solution of a class of Volterra integral equations with singular and weakly singular kernels [J] . Tang BQ, Li XF Applied mathematics and computation . 2008,第2期

机译：一类具有奇异核和弱奇异核的Volterra积分方程的解
4. Convergence analysis of the spectral method for second-kind Volterra integral equations with a weakly singular kernel [C] . Zhang Xiao-yong, Wu Huafeng International Conference on Information Technology and Management Innovation . 2013

机译：具有弱奇异内核的二种Volterra积分方程的光谱法的收敛性分析
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. Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations [O] . Michael Feischl, Gregor Gantner, Dirk Praetorius -1

机译：弱奇异积分方程的自适应IGA边界元方法的可靠高效后验误差估计
7. NUMERICAL SOLUTION OF VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY SINGULAR KERNELS WHICH MAY HAVE A BOUNDARY SINGULARITY [O] . Marek Kolk, Arvet Pedas 2009

机译：具有边界奇异性的弱奇异内核的Volterra积分方程的数值解
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

RBFs for Integral Equations with a Weakly Singular Kernel

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