A collocation meshless method based on local optimal point interpolation

This paper deals with the use of the local optimal point interpolating (LOPI) formula in solving partial di erential equations (PDEs) with a collocation method. LOPI is an interpolating formula constructed by localization of optimal point interpolation formulas that reproduces polynomials and veri es the delta Kronecker property. This scheme results in a truly meshless method that produces high quality output and accurate solutions.