@article{01HWSTKF163AGJD73A0M0QRFGJ,
  abstract     = {{A gradient reproducing kernel based stabilized collocation method (GRKSCM) to numerically solve complicated nonlinear Korteweg-de Vries (KdV) equation is proposed in this paper. The acquisition of GRK through highorder consistency conditions reduces the complexity of RK derivative operations and remarkably improves the effectiveness of the proposed method by directly forming GRK approximations. Owing to the fulfillment of highorder integration constraints, the SCM achieves exact integration in the domain and on boundaries. Von Neumann analysis is utilized to establish the stability criteria for GRKSCM when combined with forward difference temporal discretization. The effectiveness of the GRKSCM method in solving the KdV equation is investigated through six numerical examples. The examples include the motion of the single solitary wave propagation, interaction between two solitary waves and interaction among three solitary waves. Furthermore, the behavior of a two-dimensional solitary wave and the propagation of a three-dimensional solitary wave are also numerically investigated. The numerical outcomes confirm that GRKSCM provides high accuracy in comparison with analytical solutions. In addition, the invariants and error analysis show the conservation of our proposed GRKSCM method.}},
  articleno    = {{105752}},
  author       = {{Xue, Zhiyuan and Liu, Yijia and Wang, Lihua and Abdel Wahab, Magd}},
  issn         = {{0955-7997}},
  journal      = {{ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS}},
  keywords     = {{Meshfree method,Stabilized collocation method,Gradient reproducing Kernel approximations,Korteweg-de Vries equation,Conservation property,DE-VRIES EQUATION,HIERARCHICAL PARTITION,SOLITON-SOLUTIONS,FORMULATION,EVOLUTION,SCHEME,UNITY}},
  language     = {{eng}},
  pages        = {{14}},
  title        = {{A meshfree method for the nonlinear KdV equation using stabilized collocation method and gradient reproducing kernel approximations}},
  url          = {{http://doi.org/10.1016/j.enganabound.2024.105752}},
  volume       = {{164}},
  year         = {{2024}},
}

Altmetric

View in Altmetric

Web of Science

Times cited: