Local meshless method for convection dominated steady and unsteady partial differential equations

  • Vikendra SinghEmail author
  • Siraj-ul-IslamEmail author
  • R. K. Mohanty
Original Article


In this paper, we propose a mildly shock-capturing stabilized local meshless method (SLMM) for convection-dominated steady and unsteady PDEs. This work is extension of the numerical procedure, which was designed only for steady state convection-dominated PDEs (Siraj-ul-Islam and Singh in Int J Comput Methods 14(6):1750067, 2017). The proposed meshless methodology is based on employing different type of stencils embodying the already known flow direction. Numerical experiments are performed to compare the proposed method with the finite-difference method on special grid (FDSG) and other numerical methods. Numerical results confirm that the new approach is accurate and efficient for solving a wide class of one- and two- dimensional convection-dominated PDEs having sharp corners and jump discontinuities. Performance of the SLMM is found better in some cases and comparable in other cases, than the mesh-based numerical methods.


Local meshless collocation method Radial basis function Boundary layer Convection–diffusion–PDEs TVD Runge–Kutta method 



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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Mathematics and Computer ScienceSouth Asian UniversityNew DelhiIndia
  2. 2.Department of Basic SciencesFaculty of Architecture, Allied Sciences and Humanities, University of Engineering and TechnologyPeshawarPakistan

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