Optimal shape parameter in the MQ-RBF by minimizing an energy gap functional

By using the multiquadric radial basis function (MQ-RBF) method for solving the mixed boundary value problem as well as the Cauchy problem of the Laplace equation in an arbitrary plane domain, an energy gap functional (EGF) is proposed to choose the shape parameters. Upon minimizing the EGF we can pick up the optimal shape parameter and hence achieve the best accuracy of numerical solution. The performance of the minimizing EGF (MEGF) is assessed by numerical tests.