One-Dimensional Galerkin Meshless Method MATLAB Implementation

This MATLAB program implements a one-dimensional Galerkin-type meshless method. Meshless methods employ point-based approximations that can completely or partially eliminate conventional meshes, removing the need for initial mesh generation and remeshing. These methods maintain computational accuracy while significantly reducing meshing complexity. However, current meshless approximations typically lack analytical expressions and are predominantly based on Galerkin principles, resulting in higher computational costs compared to traditional finite element methods. Additionally, since meshless approximations are mostly fitting-based, handling displacement boundaries presents challenges, often addressed using Lagrange multiplier methods. The implementation demonstrates node arrangement, shape function generation, and stiffness matrix assembly techniques.