Fredholm integral equations can be solved without Fourier transforms by employing alternative methods such as numerical techniques and series expansions. The discussion highlights the integral equation of the second kind, represented as \(\varphi(t)=f(t)+\lambda\int^b_aK(t,s)\varphi(s)ds\). Participants suggest using methods like the Neumann series or iterative approaches for solutions. The consensus is that while Fourier transforms are common, they are not the only viable option for solving these equations.
PREREQUISITESMathematicians, researchers in applied mathematics, and students studying integral equations and numerical analysis will benefit from this discussion.