A convergence theorem on the iterative solution of nonlinear two-point boundary-value systems

The nonlinear two-point boundary value problem occurs quite naturally in studies in many diverse science branches. For obtaining the approaching solution of the nonlinear problem we often replace the nonlinear problem with a sequence of linear problems in such a manner that the sequence of solutions to the linear problems approach in a limiting sense the solution of the nonlinear problem. The convergence theorem proved here establishes the applying of the modified Newton's method for solving the nonlinear two-point boundary-value problem.