Accelerated monotone scheme for finite difference equations concerning steady-state prey-predator interactions (Q1085584)

In a previous paper of the authors and \textit{A. Lazer} [ibid. 8, 243-252 (1982; Zbl 0494.65052)] they have studied a monotone scheme for the numerical solution of a system of semilinear elliptic partial differential equations which determine the equilibria of the Volterra- Lotka equations describing prey-predator interactions with diffusion. Here the authors propose to combine Newton's method with the previous scheme in order to accelerate the convergence. Some theoretical results proving quadratic convergence and numerical results are given.