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A finite difference approach for solution of Burgers’ equation. (English) Zbl 1093.65081
Summary: We apply a restrictive Pade approximation classical implicit finite difference method to the Burgers’ equation with a set of initial and boundary conditions to obtain its numerical solution. The stability region and truncation error of the new method are discussed. The accuracy of the proposed method is demonstrated by the two test problems. The numerical results obtained by this method for various values of viscosity are compared with the exact solution to show the efficiency of the method. The numerical results are found in good agreement with the exact solutions.

65M06Finite difference methods (IVP of PDE)
65M15Error bounds (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
Full Text: DOI
[1] Ismail, H. N. A.; Elbarbary, E. M. E.: Restrictive Taylor’s approximation and parabolic partial differential equations. Int. J. Comput. math. 78, 73-82 (2001) · Zbl 0987.65076
[2] Ismail, H. N. A.; Elbarbary, E. M. E.; Younes, Adel Y. H.: Highly accurate method for solving initial boundary value problem for first order hyperbolic differential equations. Int. J. Comput. math. 77, 251-261 (2001) · Zbl 1001.65099
[3] Öziş, T.; Aksan, E. N.; Özdeş, A.: A finite element approach for solution of Burgers equation. Appl. math. Comput. 139, 417-428 (2003) · Zbl 1028.65106
[4] Öziş, T.; Özdeş, A.: A direct variational methods applied to Burgers equation. J. comput. Appl. math. 71, 163-175 (1996)
[5] Varog\check{}lu, E.; Finn, W. D.: Space-time finite element incorporating characteristics for the Burgers equation. Int. J. Numer. methods eng. 16, 171-184 (1980) · Zbl 0449.76076
[6] Ismail, H. N. A.; Elbarbary, E. M. E.: Restrictive Padé’s approximation and parabolic partial differential equations. Int. J. Comput. math. 66, 343-351 (1996) · Zbl 0894.65039
[7] M. Gulsu, T. Öziş, Numerical solution of Burgers’ equation with restrictive Taylor approximations, Appl. Math. Comput., in press, doi:10.1016/j.amc.2005.01.106.
[8] Ames, W. F.: Numerical methods for partial differential equations. (1992) · Zbl 0759.65059
[9] Smith, G. D.: Numerical solution of partial differential equations. (1989)
[10] Mitchell, A. R.: Computational methods in partial differential equations. (1969) · Zbl 0191.45201