Explicit and implicit meshless methods for linear advection-diffusion-typepartial differential equations

Simple, mesh/grid free, explicit and implicit numerical schemes for the sol ution of linear advection-diffusion problems is developed and validated her ein. Unlike the mesh or grid-based methods, these schemes use well distribu ted quasi-random points and approximate the solution using global radial ba sis functions. The schemes can be seen as generalized finite differences wi th random points instead of a regular grid system. This allows the computat ion of problems with complex-shaped boundaries in higher dimensions with no need for complex mesh/grid structure and with no extra implementation diff iculties. Copyright (C) 2000 John Wiley & Sons, Ltd.