Solving partial-differential algebraic equations with the fifth-Order Meshless Petrov-Galerkin Method by CS-RBFS interpolation

Document Type : Research Paper


1 Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran

2 Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin 34149-16818, Iran


In this paper, the application of the Fifth-order Meshless Local Petrov-Galerkin Method in solving the linear partial differential-algebraic equations (PDAEs) was surveyed. The Gaussian quadrature points in the domain and on the boundary were determined as centers of local sub-domains. By governing the local weak form in each sub-domain, the compactly supported radial basis functions (CS-RBFs) approximation was used as the trial function and the Heaviside step function was considered as the test function. The proposed method was successfully utilized for solving linear PDAEs and the numerical results were obtained and compared with the exact solution to investigate the accuracy of the proposed method. The sensitivity to different parameters was analyzed and a comparison with the other methods was done.


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Volume 14, Issue 3
March 2023
Pages 353-367
  • Receive Date: 12 October 2021
  • Revise Date: 09 January 2022
  • Accept Date: 11 January 2022
  • First Publish Date: 12 November 2022