Searching for an optimal shape parameter for solving a partial differential equation with the radial basis functions method

The numerical solution of partial differential equations has usually been obtained by using finite difference methods, finite element methods (FEMs), boundary elements methods or finite volume methods. In our case, we use the multiquadric radial basis function, Gershgorin's theorem and the Newton method for searching an optimal shape parameter for solving diffusion equations. More cases are presented, the results of which are compared with the results obtained by the FEM.