Meshless solution of the neutron diffusion equation by the RBF collocation method using optimum shape parameters

The meshless radial basis function collocation method is an efficient numerical technique for solving partial differential equations. The multiquadric is the most widely utilized radial function for this purpose; but it contains a shape parameter, which has a significant effect on the performance of the method. In this study, the meshless collocation method employing multiquadric as the radial function with optimum shape parameters is applied to the numerical solution of the multigroup neutron diffusion equation. The optimization of the shape parameter is performed by minimizing the Madych-Nelson function. One external and two fission source problems are solved to investigate the performance of the method. The results show that the meshless collocation method with optimized shape parameters yield a high level of accuracy with an exponential convergence rate.