A NEW APPROACH TO NUMERICAL DIFFERENTIATION AND INTEGRATION

Some new formulae for numerical differentiation and integration are de rived by using interpolatory subdivision algorithms. These interpolato ry subdivision algorithms are originally designed for the generation o f smooth curves. The main advantage of these numerical formulae is tha t they produce better numerical results if the data comes from functio ns with fractal-like derivatives. The main disadvantage of these formu lae is that they normally do not have the best approximation orders. B y using different interpolatory subdivision algorithms, higher order a pproximation formulae can be obtained. Some numerical examples are giv en to compare these formulae with the traditional high accuracy formul ae.