2009/05/28 by Hennadiy Netuzhylov, Andreas Zilian · 1 citation
Engineering · Mathematics · #Applied mathematics #Boundary element method #Boundary value problem #Collocation (remote sensing) #Collocation method #Computer science #Differential equation #Discrete mathematics #Discretization #Finite element method #Fluid Dynamics Simulations and Interactions #Geotechnical Engineering and Underground Structures #Interpolation (computer graphics) #Kernel (algebra) #Kronecker delta #Mathematical analysis #Mathematical optimization #Mathematics #Meshfree methods #Moving least squares #Numerical methods in engineering #Ordinary differential equation #Partial differential equation #Regularized meshless method #Singular boundary method
paper · doi:10.1002/nme.2638
openalex publication_date 2009/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/19
Abstract A novel space–time meshfree collocation method (STMCM) for solving systems of non‐linear ordinary and partial differential equations by a consistent discretization in both space and time is proposed as an alternative to established mesh‐based methods. The STMCM belongs to the class of truly meshfree methods, i.e. the methods that do not have any underlying mesh, but work on a set of nodes only without any a priori node‐to‐node connectivity. Instead, the neighbouring information is established on‐the‐fly. The STMCM is constructed using the Interpolating Moving Least‐squares technique, which allows a simplified implementation of boundary conditions due to fulfillment of the Kronecker delta property by the kernel functions, which is not the case for the major part of other meshfree methods. The method is validated by several examples ranging from interpolation problems to the solution of PDEs, whereas the STMCM solutions are compared with either analytical or reference ones. Copyright © 2009 John Wiley & Sons, Ltd.