  In this paper, we present a new iterative approximate method of solving
boundary value problems. The idea is to compute approximate polynomial
solutions in the Bernstein form using least squares approximation combined with
some properties of dual Bernstein polynomials which guarantee high efficiency
of our approach. The method can deal with both linear and nonlinear
differential equations. Moreover, not only second order differential equations
can be solved but also higher order differential equations. Illustrative
examples confirm the versatility of our method.
