Discrete differential operators on irregular nodes (DDIN)

A previous research made an integral mathematical contribution for obtaining local function interpolation using neighboring nodal values of the solution function. Subsequent researchers developed mesh‐free methods for Finite Element Method (FEM). This principle can also be used to obtain discrete differential operators on irregular nodes. They may be successfully applied to Finite Difference method, Moving Particle Semi‐implicit (MPS) method and Random Collocation Method (RCM). In this paper, we obtain discrete differential operators on irregular nodes and successfully apply them to solve differential equations using the RCM. We also discuss mathematical aspects of the MPS method. Copyright © 2011 John Wiley & Sons, Ltd.