Computational method for solving weakly singular Fredholm integral equations of the second kind using an advanced barycentric Lagrange interpolation formula

Document Type

Article

Publication Date

Winter 12-8-2021

Abstract

In this study, we applied an advanced barycentric Lagrange interpolation formula to fnd the interpolate solutions of weakly singular Fredholm integral equations of the sec- ond kind. The kernel is interpolated twice concerning both variables and then is trans- formed into the product of fve matrices; two of them are monomial basis matrices. To isolate the singularity of the kernel, we developed two techniques based on a good choice of diferent two sets of nodes to be distributed over the integration domain. Each set is specifc to one of the kernel arguments so that the kernel values never become zero or imaginary. The signifcant advantage of thetwo presented techniques is the ability to gain access to an algebraic linear system equivalent to the interpolant solution without applying the collocation method. Moreover, the convergence in the mean of the interpolant solution and the maximum error norm estimation are studied. The interpolate solutions of the illustrated four examples are found strongly converg- ing uniformly to the exact solutions.

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