SOLVING FOURTH-ORDER PARTIAL DIFFERENTIAL EQUATIONS USING RADIAL BASIS FUNCTION COLLOCATION METHODS

In this paper, we propose a new approach for solving fourth-order partial differential equations (PDEs) which uses an intermediate step so that fourth order PDEs can be reduced to second order PDEs. This method is simple and easy to implement. We compare the numerical result of this method to the Kansa method and the method of approximate particular solutions (MAPS). We also observe the numerical accuracy of the proposed method on the local Kansa method (LKM) and localized method of approximate particular solutions (LMAPS). Numerical results show that this method outperforms the MAPS and Kansa method in both global and local cases.