A new class of analytical solutions to nonlinear boundary value problems

This paper establishes a new class of analytical solutions for nonlinear boundary value problems defined by systems of ordinary differential equations. This class uses Bezier functions derived from Bezier curves. Three engineering examples, (1) a fully developed laminar flow in a pipe with constant surface temperature; (2) a three dimensional flow over a rotating disk; (3) a three dimensional rotating flow over a stationary disk, are solved and the analytical solution is provided. These solutions are graphically indistinguishable from the exact or numerical solutions used for comparison. The solutions are obtained through standard design optimization techniques. The approach is simple. The set up is direct. No state space formulation is necessary for handling the set of differential equations. The procedure is independent of the type or the discipline the problem belongs to. The procedure is adaptive through the selection of the order of the Bezier functions.