Mesh-Less methods to solve practical engineering problems based on inhomogeneous partial differential equation

This work concerns with the the problem of in accuracy of derivatives of RBFs on the domain boundary when a direct collocation method is used. This problem appears clearly in the convection dominant problems for second instability. The mismatch of the interpolation scheme with the nature of the physical problem is the cause of that problem. Two approaches are derived for addressing aforementioned problem. The first approach adopts changing the interpolation scheme as an answer to aforementioned problem. By this approach a proposed shape function is developed as a linear interpolating function of both MLS and RBFs on the same support domain. The proposed shape function seems to be a tuning shape function between two points on opposite surfaces; one of them is constructed by MLS and the other is constructed by RBFs. The proposed shape function is regularized through a control parameter 11 which takes different values in the domain [0, I].