TY - JOUR ID - 9464 TI - Meshless local radial point interpolation (MLRPI) to two dimensional wave equation with Neumann’s boundary conditions JO - Computational Methods for Differential Equations JA - CMDE LA - en SN - 2345-3982 AU - Shivanian, Elyas AU - Hosseini, Mostafa AU - Rahimi, Asghar AD - Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran Y1 - 2020 PY - 2020 VL - 8 IS - 1 SP - 155 EP - 172 KW - Meshless local radial point interpolation (MLRPI) KW - Local weak formulation KW - Radial basis function KW - 2-D wave equation KW - Neumann’s boundary conditions KW - Finite difference DO - 10.22034/cmde.2019.9464 N2 - In this article, the meshless local radial point interpolation (MLRPI) methods are applied to simulate two dimensional wave equation subject to given appropriate initial and Neumann’s boundary conditions. In MLRPI method, all integrations are carried out locally over small quadrature domains of regular shapes such as square or circle. The radial point interpolation method is proposed to construct shape functions for MLRPI. A weak formulation with a Heaviside step function transforms the set of governing equations into local integral equations on local sub domains where Neumann’s boundary condition is imposed naturally. A two-step time discretization method with the help of Crank-Nicolson technique is employed to approximate the time derivatives. Convergence studies in the numerical example show that MLRPI method possesses excellent rates of convergence. UR - https://cmde.tabrizu.ac.ir/article_9464.html L1 - https://cmde.tabrizu.ac.ir/article_9464_2436e78017e3fbb60ea238e23b3c4f75.pdf ER -