Radial basis functions as approximate particular solutions: review of recent progress
Solution of Poisson type differential equations can be achieved by finding an approximate particular solution to the forcing term followed by a boundary element method or more simply by using a boundary collocation method. The approximate particular solution is often found by using radial basis functions approximations to the forcing function. The advantage of radial basis functions is they involve a single independent variable regardless of the dimension of the problem. They prove particularly attractive when the domain cannot be expressed as product domains of lower dimensions. This paper provides a review of some of the recent progress in this field (in connection with the solution of Poisson type differential equations) together with some new results. Particular emphasis will be on the solution of non-linear and time dependent differential equations.
radial basis functions approximate particular solutions poisson type differential equations