Abstract: This paper presents a novel analytical method for obtaining exact solutions of  Hammerstein integral equations with degenerate kernels. Subsequently, this approach is  systematically extended to equations with general kernels, yielding a convergent numerical  approximation whose theoretical analysis establishes sufficient conditions for convergence  and provides explicit error bounds. Numerical experiments are conducted to demonstrate the efficiency and accuracy of the proposed method, showing favorable performance compared to existing techniques.

Key words: Hammerstein integral equation, Degenerate kernel, Exact solution, Numerical , solution, Error analysis