An interpolating reproducing kernel particle method for two-dimensional scatter points

An interpolating reproducing kernel particle method for two-dimensional (2D) scatter points is introduced. It eliminates the dependency of gridding in numerical calculations. The interpolating shape function in the interpolating reproducing kernel particle method satisfies the property of the Kronecker delta function. This method offers a mathematics basis for recognition technology and simulation analysis, which can be expressed as simultaneous differential equations in science or project problems. Mathematical examples are given to show the validity of the interpolating reproducing kernel particle method.