Numerical Study of Two-Dimensional Burger’s Equation: The Phenomenon of the Fall of Sediment Particles Using Incremental Differential Quadrature Method

2021 ◽  
Author(s):  
Mohammad Vaghefi ◽  
Hossein Rahideh ◽  
Sam Boveiri ◽  
Iman Rezaei
Keyword(s):  
Numerical Study ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Two Dimensional ◽  
Quadrature Method ◽  
Burger's Equation ◽  
Burger’S Equation ◽  
Sediment Particles

A numerical study of two-dimensional coupled systems and higher order partial differential equations

2019 ◽  
Vol 12 (05) ◽  
pp. 1950071
Author(s):  
R. Rohila ◽  
R. C. Mittal
Keyword(s):  
Differential Equations ◽  
Numerical Study ◽  
Differential Quadrature Method ◽  
Bernstein Polynomials ◽  
Differential Quadrature ◽  
Coupled Systems ◽  
Two Dimensional ◽  
Quadrature Method ◽  
Grid Points ◽  
The Stability

In this paper, a new approach and methodology is developed by incorporating differential quadrature technique with Bernstein polynomials. In differential quadrature method, approximations are done in a way that the derivatives of the function are replaced by a linear sum of functional values at the grid points of the given domain. In Bernstein differential quadrature method (BDQM), Bernstein polynomials are employed for spatial discretization so that a system of ordinary differential equations (ODE’s) is obtained which is solved by SSPRK-43 method. The stability of the method is also studied. The accuracy of the present method is checked by performing numerical experiments on two-dimensional coupled Burgers’ and Brusselator systems and fourth-order extended Fisher Kolmogorov (EFK) equation. Implementation of the method is very easy, efficient and capable of reducing the size of computational efforts.

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