This research presents a comprehensive comparative framework for three enhanced numerical methods for solving Fredholm Integral Equations (FIEs): the Nyström method improved with spline Gaussian quadrature, the Collocation method using Müntz-Legendre wavelet basis, and the Picard iterative scheme. A unified experimental framework was developed in MATLAB to evaluate the performance of these methods across a wide range of benchmark problems, including both linear and nonlinear, well-posed and ill-posed equations. The work aims to provide practical, empirically-supported guidelines for selecting the optimal numerical approach based on specific problem characteristics................... Keywords: ..............Fredholm Integral Equations, Numerical Analysis, Nyström Method, Collocation Method, Picard Iteration, Ill-Posed Problems, Tikhonov Regularization, Spline Quadrature, Wavelet Basis, Hammerstein Equation.