Superconvergent kernel functions approaches for the second kind Fredholm integral equations

摘要

By employing the kernel functions with the form of piecewise polynomials in the Sobolev reproducing kernel Hilbert spaces (RKHSs), a globally superconvergent numerical technique is proposed to solve the second kind linear integral equations of Fredholm type. This method has an order of global convergence O(h~4) and O(h~6) based on the kernel functions in the Sobolev RKHSs H~1 and H~2, respectively. Three linear Fredholm integral equations, one Volterra-Fredholm integral equation and one nonlinear Fredholm integral equation are numerically solved by the present approach to verify the superconvergence and effectiveness.