Barycentric Lagrange Interpolation in Matrix-Vector Versions for solving Love’s Integral Equations

Abstract

In this paper, we solve two integral equations of Love’s type that have many applications, especially in electrostatic systems. The approach of the solution is based on an innovative technique using matrix algebra for the barycentric Lagrange interpolation. The unknown function is expressed through the product of four matrices, one of which is a square matrix in which each row expresses the coefficients of one barycentric function. The kernel is interpolated twice, so we get the product of five matrices. One of these matrices is the most important matrix in the solution’s procedure. As it expresses the functional values of the kernel at the interpolation nodes for the two variables. Additionally, we derive an equivalent linear algebraic system to the solution by substituting the matrix-vector barycentric interpolated unknown function together with the double interpolation kernel into both sides of the integral equation. The obtained results converge strongly with the approximate analytical solutions. In addition to being uniformly approximated, continuous, and even, which proves the validity of the solution by the presented method. MSC code: 00A69