A Novel Wavelet-based Approximation Scheme for the Approximate Solution/Source of Fredholm Integral Equation of the Second Kind with Variable Coefficient and the Pseudo-Logarithmic Kernels

This study introduces an efficient orthonormal polynomial wavelet-based approximation scheme for solving Fredholm integral equations of the second kind with logarithmic/pseudo-logarithmic singular kernels. The method exhibits high accuracy and computational efficiency and seems applicable simultaneously when the exact solution or the source term is unknown to be determined. The examples tested here validate the accuracy and effectiveness of the scheme proposed here.