Bezier formulation of multistep algorithms

Predictor-based integration formulas are presented by formulating the solution function as a vectored value Bernstein polynomial, namely a Bezier function. The Bezier function subdivision theorem leads to a predictor evaluation algorithm for the next solution point using de Casteljau´s iterative control vertex generation technique. It is shown that the convergence of the algorithms is a consequence of the use of Bernstein uniform approximation basis and that the de Casteljau predictor evaluation scheme leads to a computationally simple estimate of the local truncation error