A double boundary collocation Hermitian approach for the solution of steady state convection–diffusion problems

In this article a double boundary collocation approach based on the meshless radial basis function Hermitian method (symmetric method) is proposed and compared with the conventional single collocation. In the double boundary collocation approach, at the boundary collocation points the boundary condition and the governing partial differential equation are required to be satisfied simultaneously instead of only the boundary condition as required in the single collocation. We are able to carry out this type of algorithm due to the robustness of the proposed Hermite interpolation scheme, in which the resulting matrix will be non-singular as long as the partial differential operators applied to each point are linearly independent, even if in a single node we impose two different differential conditions. The results obtained with this new method are characterized by a higher precision especially for the prediction of the fluxes at the boundaries. This is due to the higher order of continuity of the approximation at the boundary points imposed by the double collocation.