The Shooting Method for Non-standard Boundary Value Problem

The paper deals with a method for solving the non-standard two-point boundary value problem in which the number of boundary conditions is greater than the number of first-order ODEs containing a certain number of unknown parameters. The total number of the unknown parameters depends on the number of boundary conditions and the way they are distributed at both ends of the domain. The presented method consists in the replacement of the boundary value problem by the initial value problem formulated with the use of sensitivity functions. The general discussion has been illustrated by numerical example consisting of two first-order differential equations and four boundary conditions. The difference between the standard and non-standard boundary value problems consists in the size of the initial value problem that needs to be solved.