Despite the significant advances in the numerical solution of nonlinear
boundary value problems, most of the existing methods still encounter
with a high sensitivity to the initial guess. The aim of this paper is
to propose a less sensitive robust numerical scheme for accurate
solution of sensitive boundary value problems. For this purpose, an
orthogonal collocation approach for discretization of the problem is
utilized. Thereby, the problem is converted to the solution of nonlinear
algebraic equations. However, due to the difficulties of solving the
obtained system of nonlinear equations, particularly in providing the
proper initial guess, the obtained system of equations is transferred to
an optimization problem in which the values of the solution at
collocation points are considered as decision parameters. The method
finds good results even using not good initial guess for decision
parameters and even using a small number of discretization points.
Numerical results of two benchmark examples are presented and the
efficiency of the method is reported.