Convergence analysis of Legendre spectral projection methods for Hammerstein integral equations of mixed type (Q500015)

The authors consider the Fredholm integral equation of Hammerstein type \[ x(t) - \sum_{i=1}^m \int_{-1}^1 k_i(t,s) \psi_i(s, x(s)) ds = f(t) \] in the spaces \(C[-1,1]\) and \(L_2(-1,1)\). For numerically solving this equation, they suggest to use two methods based on Legendre polynomial expansions of the unknown function; specifically a Galerkin method and a collocation method. Under suitable assumptions, some error estimates are derived.