The Barycentric Lagrange Interpolation via Maclaurin Polynomials for Solving the Second Kind Volterra Integral Equations

A modified formula of the traditional Barycentric Lagrange interpolation is established and applied for solving the second kind Volterra integral equations. The main goal is improving the performance of the traditional formula to minimize the round-off error. For this goal, we expand each Barycentric function into Maclaurin polynomial so that the interpolant unknown function, the given function, and the kernel can be expressed through a monomial basis polynomial matrix. Moreover, by substituting the interpolant unknown function into both sides of the integral equation, the solution is reduced to an equivalent algebraic linear system in matrix form. Convergence in the mean and the maximum norm error estimation are studied. From the solution of illustrated four examples, we observed that the interpolant solutions equal to the exact solutions if the kernel and the given functions are analytic while extraordinarily converge to the exact solutions for non-algebraic functions, which ensures the accuracy and authenticity of the presented method.