scholarly journals Numerical solution of two dimensional coupled viscous Burger equation using modified cubic B-spline differential quadrature method

AIP Advances ◽  
2014 ◽  
Vol 4 (11) ◽  
pp. 117134 ◽  
Author(s):  
H. S. Shukla ◽  
Mohammad Tamsir ◽  
Vineet K. Srivastava ◽  
Jai Kumar
Keyword(s):  
Numerical Solution ◽  
Burger Equation ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Two Dimensional ◽  
Quadrature Method ◽  
B Spline

Modified cubic B-spline differential quadrature method for numerical solution of three-dimensional coupled viscous Burger equation

2016 ◽  
Vol 30 (11) ◽  
pp. 1650110 ◽  
Author(s):  
H. S. Shukla ◽  
Mohammad Tamsir ◽  
Vineet K. Srivastava ◽  
Mohammad Mehdi Rashidi
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Burger Equation ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Differential Quadrature ◽  
Solution Stability ◽  
Quadrature Method ◽  
B Spline

In this paper, we propose a modified cubic B-spline differential quadrature method (MCB-DQM) to solve three-dimensional (3D) coupled viscous Burger equation with appropriate initial and boundary conditions. In this method, modified cubic B-spline is treated as a basis function in the differential quadrature method (DQM) to compute the weighting coefficients. In this way, the Burger equation is reduced into a system of ordinary differential equations. An optimal strong stability-preserving Runge–Kutta (SSP-RK) method is employed to solve the resulting system of ordinary differential equations. In order to illustrate the accuracy and efficiency of the proposed method, a numerical problem is considered. From the numerical experiment, it is found that the computed result is in good agreement with the exact solution. Stability analysis of the method is also carried out using the matrix stability analysis method and found to be unconditionally stable.

scholarly journals A Composite Algorithm for Numerical Solutions of Two-Dimensional Coupled Burgers’ Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Vikas Kumar ◽  
Sukhveer Singh ◽  
Mehmet Emir Koksal
Keyword(s):  
Finite Difference ◽  
Exact Solutions ◽  
Numerical Solutions ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Dirichlet Boundary Conditions ◽  
Two Dimensional ◽  
Quadrature Method ◽  
B Spline ◽  
Burgers Equations

In this study, a new composite algorithm with the help of the finite difference and the modified cubic trigonometric B-spline differential quadrature method is developed. The developed method was applied to two-dimensional coupled Burgers’ equation with initial and Dirichlet boundary conditions for computational modeling. The established algorithm is better than the traditional differential quadrature algorithm proposed in literature due to more smoothness of cubic trigonometric B-spline functions. In the development of the algorithm, the first step is semidiscretization in time with the forward finite difference method. Furthermore, the obtained system is fully discretized by the modified cubic trigonometric B-spline differential quadrature method. Finally, we obtain coupled Lyapunov systems of linear equations, which are analyzed by the MATLAB solver for the system. Moreover, comparative study of these solutions with the numerical and exact solutions which are appeared in the literature is also discussed. Finally, it is found that there is good suitability between exact solutions and numerical solutions obtained by the developed composite algorithm. The technique can be extended for various multidimensional Burgers’ equations after some modifications.

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