Application of Gaussian quadrature on the numerical solution of the time kernel equation

Abstract

The time kernel equation is transformed into a system of integral equations and the Gauss-Legendre quadrature rule was applied. The accuracy of the method is gauged by comparing it with the analytically corrected time kernel factor. The results show that the approximation via the quadrature method is correct up to the third order correction. Discussion on the advantages and disadvantages of the method is also presented. Resolving the disadvantages of the method is also described.