  We present a new third-order, semi-discrete, central method for approximating
solutions to multi-dimensional systems of hyperbolic conservation laws,
convection-diffusion equations, and related problems. Our method is a
high-order extension of the recently proposed second-order, semi-discrete
method in [16].
  The method is derived independently of the specific piecewise polynomial
reconstruction which is based on the previously computed cell-averages. We
demonstrate our results, by focusing on the new third-order CWENO
reconstruction presented in [21]. The numerical results we present, show the
desired accuracy, high resolution and robustness of our method.

Numerical Analysis;Analysis of PDEs