A Spline Method for Solving Two-Dimensional Fredholm Integral Equation of Second Kind with the Hypersingular Kernel (Journal of Computational Mathematics, 2001)
The purpose of this paper is to adopt the quasi-interpolating operators in multivariate spline space $S^1_2(Δ^{2*}_{mn})$ 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.