A pseudospectral method for Hammerstein equations (Q1916825)

The paper is concerned with the numerical solution of the Hammerstein integral equation \[ y(t) - \int^1_0k(t,s)g \bigl(s,y(s) \bigr)ds=f(t), \quad t\in[-1,1], \tag{1} \] with \(g\) nonlinear in \(y\). The proposed method is applied not to equation (1), but rather to an equivalent equation \(z(t) = g(t,y(t))\), where \(z\) is approximated by algebraic polynomials, with coefficients determined by collocating at the Gauss-Legendre-Lobatto nodes. The authors establish uniform convergence of the approximate solutions and present numerical examples.