Nonlinear BVP

The Bézier Solutions are Analytic in all examples

Blasius Problem

The non-dimensional laminar velocity flow over a flat plate

Rotational Flow

A set of three nonlinear couple ordinary differential equations describing free rotational flow of fluid

Numerical and Bézier Solution

Laminar Flow - Channel Entrance

The laminar developing flow in the entrance of a 2D channel (three coupled nonlinear differential equations)

Numerical and Bézier Solution

Numerical (FEA): Input u is flat and v is zero - (the FEA solution cheats setting wall u to zero at entrance)

Kortweg-de Vries Equation

This special differential is a challenge to estimate with polynomials since it is a single sharp hump. The exact solution is known and included below.

Exact and Bézier Solution

Exact

Bézier (No-slip conditions take a finite length to develop because there is no infinite velocity gradient)

Bézier