Solves the 2.nd order ODE d²y⁄dx² = −1 ⁄ (1 + y)² with given initial [(x_i, y_i)] and final [(x_f, y_f)] points ([Vesely, 2005]). The absence of the value of the initial derivative, y'_i, makes it a BVP, boundary value problem. (The corresponding IVP, initial value problem, would, for x_i, have y_i and y'_i both given.) The problem is solved via shooting with an RK4 numerical integration. The (univariate) search for y'_i is done by the Fibonacci method in the (bracketing) search interval given. The solution reported (op. cit.) is y'_i = 0.437.

This BVP is a "Dirichlet condition" type problem. A "Dirichlet condition" problem has two y values specified, and a "Neumann condition" problem has two y' values specified, "mixed condition" otherwise.

Plots three curves versus x: y, y', and y".

• Vesely, F., "Boundary Value Problems", 4.3.1 Shooting Method (=), Universität Wien.

• Google boundary value problem

• 1796-08-28: Bienaymé, Irenée-Jules (1878-10-19).