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Volume 19, Issue 3
A Spline Method for Solving Two-Dimensional Fredholm Integral Equation of Second Kind with the Hypersingular Kernel

Ren-Hong Wang & You Lu

J. Comp. Math., 19 (2001), pp. 225-230.

Published online: 2001-06

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  • Abstract

The purpose of this paper is to adopt the quasi-interpolating operators in multivariate spline space $S^1_2(\Delta^{2*}_{mn})$ to solve two-dimensional Fredholm Integral Equations of second kind with the hypersingular kernels. The quasi-interpolating operators are put forward in ([7]). Based on the approximation properties of the operators, we obtain the uniform convergence of the approximate solution sequence on the Second Kind Fredholm intergral equation with the Cauchy singular kernel function.

  • Keywords

Hypersingular integral, Finite-part integral, Quasi-interpolating operator, Nonuniform type-2 triangulation.

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COPYRIGHT: © Global Science Press

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@Article{JCM-19-225, author = {Wang , Ren-Hong and Lu , You}, title = {A Spline Method for Solving Two-Dimensional Fredholm Integral Equation of Second Kind with the Hypersingular Kernel}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {3}, pages = {225--230}, abstract = {

The purpose of this paper is to adopt the quasi-interpolating operators in multivariate spline space $S^1_2(\Delta^{2*}_{mn})$ to solve two-dimensional Fredholm Integral Equations of second kind with the hypersingular kernels. The quasi-interpolating operators are put forward in ([7]). Based on the approximation properties of the operators, we obtain the uniform convergence of the approximate solution sequence on the Second Kind Fredholm intergral equation with the Cauchy singular kernel function.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8975.html} }
TY - JOUR T1 - A Spline Method for Solving Two-Dimensional Fredholm Integral Equation of Second Kind with the Hypersingular Kernel AU - Wang , Ren-Hong AU - Lu , You JO - Journal of Computational Mathematics VL - 3 SP - 225 EP - 230 PY - 2001 DA - 2001/06 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8975.html KW - Hypersingular integral, Finite-part integral, Quasi-interpolating operator, Nonuniform type-2 triangulation. AB -

The purpose of this paper is to adopt the quasi-interpolating operators in multivariate spline space $S^1_2(\Delta^{2*}_{mn})$ to solve two-dimensional Fredholm Integral Equations of second kind with the hypersingular kernels. The quasi-interpolating operators are put forward in ([7]). Based on the approximation properties of the operators, we obtain the uniform convergence of the approximate solution sequence on the Second Kind Fredholm intergral equation with the Cauchy singular kernel function.

Wang , Ren-Hong and Lu , You. (2001). A Spline Method for Solving Two-Dimensional Fredholm Integral Equation of Second Kind with the Hypersingular Kernel. Journal of Computational Mathematics. 19 (3). 225-230. doi:
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