A New Meshless Collocation Method for Partial Differential Equations

The book presents a novel collocation meshless method for solving Partial Differential Equations (PDEs) using scattered point distributions. It details the construction of meshless shape functions through polynomial interpolation on selected nodes, maintaining properties similar to the Finite Element Method. The methodology incorporates a nearest neighbor algorithm for node selection and a Gauss-Jordan pivot-based search for optimal stencil selection, ensuring efficient numerical treatment. Various schemes for elliptic, parabolic, and hyperbolic PDEs are explored, with extensive computational results analyzed.