Numerical solution of Burgers’ equation by cubic B-spline quasi-interpolation

2009 ◽  
Vol 208 (1) ◽  
pp. 260-272 ◽  
Author(s):  
Chun-Gang Zhu ◽  
Ren-Hong Wang
Keyword(s):  
Numerical Solution ◽  
Burgers Equation ◽  
B Spline

scholarly journals Numerical solution of time fractional Burgers equation

2015 ◽  
Vol 7 (2) ◽  
pp. 167-185 ◽  
Author(s):  
A. Esen ◽  
O. Tasbozan
Keyword(s):  
Galerkin Method ◽  
Numerical Solution ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Absolute Error ◽  
B Spline

Abstract In this article, the time fractional order Burgers equation has been solved by quadratic B-spline Galerkin method. This method has been applied to three model problems. The obtained numerical solutions and error norms L2 and L∞ have been presented in tables. Absolute error graphics as well as those of exact and numerical solutions have been given.

scholarly journals Numerical study of the Benjamin-Bona-Mahony-Burgers equation

2017 ◽  
Vol 35 (1) ◽  
pp. 127 ◽  
Author(s):  
M. Zarebnia
Keyword(s):  
Stability Analysis ◽  
Numerical Solution ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Numerical Study ◽  
Numerical Results ◽  
Spline Collocation ◽  
Unconditionally Stable ◽  
B Spline ◽  
Analysis Technique

In this paper, the quadratic B-spline collocation methodis implemented to find numerical solution of theBenjamin-Bona-Mahony-Burgers (BBMB) equation. Applying theVon-Neumann stability analysis technique, we show that the method is unconditionally stable. Also the convergence of the method is proved. The method is applied on some testexamples, and numerical results have been compared with theexact solution. The numerical solutions show theefficiency of the method computationally.

scholarly journals Two Different Methods for Numerical Solution of the Modified Burgers’ Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Seydi Battal Gazi Karakoç ◽  
Ali Başhan ◽  
Turabi Geyikli
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stability Analysis ◽  
Numerical Solution ◽  
Nonlinear Term ◽  
Burgers Equation ◽  
Unconditionally Stable ◽  
Von Neumann ◽  
B Spline ◽  
Modified Burgers Equation

A numerical solution of the modified Burgers’ equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computingL2andL∞error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis is also given for the DQM.

scholarly journals B-spline collocation methods for numerical solutions of the Burgers' equation

2005 ◽  
Vol 2005 (5) ◽  
pp. 521-538 ◽  
Author(s):  
Idris Dag ◽  
Dursun Irk ◽  
Ali Sahin
Keyword(s):  
Numerical Solution ◽  
Collocation Method ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Collocation Methods ◽  
Test Problems ◽  
Spline Collocation ◽  
B Spline ◽  
Spline Collocation Method ◽  
Burgers Equations

Both time- and space-splitted Burgers' equations are solved numerically. Cubic B-spline collocation method is applied to the time-splitted Burgers' equation. Quadratic B-spline collocation method is used to get numerical solution of the space-splitted Burgers' equation. The results of both schemes are compared for some test problems.

Numerical solution of Burgers’ equation by B-spline collocation

2016 ◽  
Vol 27 (7-8) ◽  
pp. 1287-1293 ◽  
Author(s):  
M. Yousefi ◽  
J. Rashidinia ◽  
M. Yousefi ◽  
M. Moudi
Keyword(s):  
Numerical Solution ◽  
Burgers Equation ◽  
Spline Collocation ◽  
B Spline

scholarly journals Error analysis of the numerical solution of the Benjamin-Bona-Mahony-Burgers equation

2019 ◽  
Vol 38 (3) ◽  
pp. 177-191
Author(s):  
M. Zarebnia ◽  
R. Parvaz
Keyword(s):  
Error Analysis ◽  
Numerical Solution ◽  
Analytical Solutions ◽  
Burgers Equation ◽  
Numerical Results ◽  
Spline Collocation ◽  
Unconditionally Stable ◽  
B Spline ◽  
Collocation Scheme

In this paper, the B-spline collocation scheme is implemented to find numerical solution of the nonlinear Benjamin-Bona-Mahony-Burgers equation. The method is based on collocation of quintic B-spline. We show that the method is unconditionally stable. Also the convergence of the method is proved. The method is applied on some test examples, and the numerical results have been compared with the analytical solutions. The $L_\infty$ and $L_2$ in the solutions show the efficiency of the method computationally.

Sign in / Sign up

Export Citation Format

Share Document