Abstract
An efficient numerical iterative method is constructed for the static deflection of an infinite beam on a nonlinear elastic foundation. The proposed iterative scheme consists of quasilinear method (QLM) and Green's function technique. The QLM translates the nonlinear ordinary differential equation into iterative linear ordinary differential equation. The successive iterations of quasilinear form of ordinary differential equation (ODE) show the quadratic convergence if an initial guess is chosen in the neighbourhood of true solution. The Green's function technique converts the differential operator into an integral operator and the integral operator is approximated by discrete summation which finally gives us an iterative formula for the resulting set of algebraic equations.The numerical validity and efficiency are proved by simulating some nonlinear problems.