A numerical solution of the Burgers’ equation using septic B-splines

Trigonometric quadratic B-spline subdomain Galerkin algorithm for the Burgers’ equation

“…These are documented at some selected times in Table 1. The results obtained by present scheme can be compared with ones given in the works [17][18][19][20][21]26] in the same table 1. From this table we conclude that the proposed algorithm for finding the shock wave solution of the Burgers' equation gives almost the same accuracy with some others.…”

“…Various degree B-splines have been used to construct some variant of numerical methods for finding the numerical solutions of the Burgers' equations. Some of these are: Galerkin finite element method [16,18,26,32,40,41], least square method [31], collocation method [19,20,27,28,30,36,38,42], finite difference method [17], differential quadrature method [33,35], method based on the cubic B-spline quasi interpolant [34,39], Taylor-Galerkin and Taylor-collocation methods [37], etc.…”

Application of the Non-Polynomial Spline Approach to the Solution of the Burgers Equation'

“…In the past few years a great deal of efforts has been expended to study the equation (1) as well as other forms of this partial differential equation, both theoretically and numerically, see for example, [3][4][5][6][7][8][9][10][11].…”

A New Approximation Method with High Order Accuracy

“…Spline solutions of differential equations are implemented in many studies. B-splines of various degrees in the collocation and Galerkin methods were introduced for the numerical solutions of partial differential equations (PDEs) such as Burgers' equation in [10][11][12][13][14][15][16]. Zhu and Wang [17] applied the cubic B-spline quasi-interpolation as a spatial approximation scheme, and a low order explicit finite difference method as a temporal approximation scheme to solve Burgers' equation, and found that the numerical results are in good agreement with exact solutions.…”