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A meshless approach for solution of Burgers' equation

Hashemian, A ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.1016/j.cam.2007.08.014
  3. Publisher: 2008
  4. Abstract:
  5. A new meshless method called gradient reproducing kernel particle method (GRKPM) is proposed for numerical solutions of one-dimensional Burgers' equation with various values of viscosity and different initial and boundary conditions. Discretization is first done in the space via GRKPM, and subsequently, the reduced system of nonlinear ordinary differential equations is discretized in time by the Gear's method. Comparison with the exact solutions, which are only available for restricted initial conditions and values of viscosity, approves the efficacy of the proposed method. For challenging cases involving small viscosities, comparison with the results obtained using other numerical schemes in the literature further attests the desirable features of the presented methodology. © 2007 Elsevier B.V. All rights reserved
  6. Keywords:
  7. Boundary conditions ; Boundary value problems ; Difference equations ; Differential equations ; Differentiation (calculus) ; Hydrodynamics ; Nonlinear equations ; Numerical analysis ; Ordinary differential equations ; Solutions ; Viscosity ; Burger's equations ; Discretization ; Exact solutions ; Initial conditions ; Meshless approach ; Meshless method (MM) ; Numerical schemes ; Numerical solutions ; One-dimensional ; Reproducing kernel particle method (RKPM) ; Numerical methods
  8. Source: Journal of Computational and Applied Mathematics ; Volume 220, Issue 1-2 , 2008 , Pages 226-239 ; 03770427 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0377042707004384