General Parameter Mapping Technique—A Procedure for Solution of Non-linear Boundary Value Problems Depending on an Actual Parameter

A new general method is developed to obtain the dependence of the solution of a non-linear boundary value problem on an arbitrary actual parameter of the problem under consideration. This technique is essentially an application of the implicit function theorem (Davidenko's approach) to the solution of non-linear boundary value problems. The procedure suggested requires the integration of sets of ordinary differential equations (initial value problems) with the right-hand sides obtained from a solution of a certain set of auxiliary differential equations.