On the effect of order of radial basis functions in the solution of partial differential equations

This paper investigates the effects of varying the order of RBF´s. It has been found that as the order is increased, the accuracy also increases. The accuracy was even shown to increase to the extent that less than 10% of the basis functions were required to obtain the same level of accuracy. However, it is also found that increasing the order also generally increases the condition number of the system matrix. There is still significant research that needs to be done with RBF´s and meshless algorithms. Some areas of future work include looking at preconditioning schemes, implementing boundary conditions, etc.