A New Computational Method for Solving Weakly Singular Fredholm Integral Equations of the First Kind

A new computational technique is given for the numerical solution of Fredholm integral equation of the first kind with a singular density function and a weakly singular logarithmic kernel. The singular density function and the given data function are approximated by using monic Chebyshev polynomials. The singularity of the kernel is treated by expanding the kernel into Maclaurin polynomial of the first degree about the singular parameter. Moreover, an adaptive Gauss-Legendre formula is applied. It turns out from the illustrated example that the presented method clearly simplifies the computations, saves time, and ensures a superior accuracy of the solution.