Abstract
In this paper, a novel meshfree method employing the idea of IDO (Interpolated Differential Operator) scheme is presented. This method makes use of advantages of the both IDO scheme and Meshfree method, and can solve PDEs accurately even using "irregular" grids. For this purpose, the generalized moving least squares approximation that can construct the Hermite type approximation space is adopted. In order to demonstrate the potential of the proposed MADO (Meshfree Approximated Differential Oparator) scheme, advection problems are solved. Finally, the accuracy, the convergence rate and the computational efficiency are investigated by comparing with the conventional methods and satisfactory results are obtained.
