MQ-Radial Basis Functions Center Nodes Selection with PROMETHEE Technique

In this paper, we decide to select the best center nodes of radial basis functions by applying the Multiple Criteria Decision Making (MCDM) techniques. Two methods based on radial basis functions to approximate the solution of partial differential equation by using collocation method are applied. The first is based on the Kansa's approach, and the second is based on the Hermite interpolation. In addition, by choosing five sets of center nodes: Uniform grid, Cartesian, Chebyshev, Legendre and Legendre-Gauss-Lobato (LGL) as alternatives and achieving the error, the condition number of interpolation matrix and memory time as criteria, rating of cases with the help of PROMETHEE technique is obtained. In the end, the best center nodes and method is selected according to the rankings. This ranking shows that Hermite interpolation by using non-uniform nodes as center nodes is more suitable than Kansa's approach with each center node.