Ahmad Shirzadi

The meshless methods are vigorous and efficient algorithms especially in high dimensions for the numerical solution of PDEs (PIDEs). The thesis begins with a review of some famous numerical methods for solving PDEs. Then some local meshless methods and basic concepts of meshless methods are presented. Afterwards by proposing the use of local weak form of governing equations on local subsystems, the finite collocation method is improved and implemented for solving heat transfer problem in elliptic fins. Another part of issues presented in the present thesis is to investigate the radial basis function finite difference methods and implemention of this method for numerical solution of Stock-Darcy equations. One of the main issues in local meshless methods is the optimal selection of stencil nodes and reducing the computation cost of theis methods. In chapter five of this thesis, a new strategy based on QR decomposition is used for optimal selection of nodal points in the radial basis function finite difference method and the method applied for numerical solution of elliptic and parabolic interface problems.