Numerical solutions of the coupled Burgers’ equation by the Galerkin quadratic B-spline finite element method

2013 ◽  
Vol 36 (17) ◽  
pp. 2403-2415 ◽  
Author(s):  
S. Kutluay ◽  
Y. Ucar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
B Spline ◽  
Spline Finite Element ◽  
Coupled Burgers Equation ◽  
Element Method ◽  
Spline Finite Element Method

scholarly journals An application of cubic B-Spline finite element method for the Burgers` equation

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 195-202
Author(s):  
Emine Aksan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Burgers Equation ◽  
B Spline ◽  
Linear Pde ◽  
Non Linear ◽  
Spline Finite Element ◽  
Linear Ode ◽  
Element Method ◽  
Spline Finite Element Method

It is difficult to achieve exact solution of non-linear PDE, directly. Sometimes, it is possible to convert non-linear PDE into equivalent linear PDE by applying a convenient transformation. Hence, Burgers? equation replaces with heat equation by means of the Hope-Cole transformation. In this study, Burgers? equation was converted to a set of non-linear ODE by keeping non-linear structure of Burgers? equation. In this case, solutions for each of the non-linear ODE were obtained by the help of the cubic B-spline finite element method. Model problems were considered to verify the efficiency of this method. Agreement of the solutions was shown with graphics and tables.

scholarly journals Numerical solutions of the improved boussinesq equation by the galerkin quadratic B-spline finite element method

Filomat ◽  
2018 ◽  
Vol 32 (16) ◽  
pp. 5573-5583 ◽  
Author(s):  
Berat Karaagac ◽  
Yusuf Ucar ◽  
Alaattin Esen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boussinesq Equation ◽  
Numerical Solutions ◽  
Blow Up ◽  
Test Problems ◽  
B Spline ◽  
Spline Finite Element ◽  
Element Method ◽  
Spline Finite Element Method

In this paper, we are going to obtain numerical solutions of the improved Boussinesq equation with the aid of Galerkin quadratic B-spline finite element method. To test the accuracy and efficiency of the current method, four test problems have been used. These are solitary wave movement, interaction of two solitary waves, wave break-up and blow-up of solutions. Their results have been compared with those available in the literature for different values of space and time steps. Also, the error norms L2 and L1 have been computed and presented in comparison.

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