On a Numerical Method for Constructing a Positive Solution of the Two-Point Boundary-Value Problem for a Second-Order Nonlinear Differential Equation

An iterative method is proposed for finding an approximation to the positive solution of the two-point boundary-value problem
$$ y''+c(x)y^m=0,\quad 0<x<1,\qquad y(0)=y(1)=0, $$
where $m=\mathrm{const}>1$ and $c(x)$ is a continuous nonnegative function on $[0,1]$. The convergence of this method is proved. An error estimate is also obtained.