A collocation solution for burgers equation using quadratic B-spline finite elements

International Journal of Computer Mathematics

Volumn 80, Issue 7, 2003, Pages 931-938

  Raslan, K R ^a  

^a Assiut Branch   (Egypt)

Author keywords

Burgers equations; Collocation; Quadratic B spline

Indexed keywords

COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; FLUID DYNAMICS; NUMERICAL METHODS; PROBLEM SOLVING;

BURGERS EQUATIONS; COLLOCATION; QUADRATIC B-SPLINES;

LINEAR EQUATIONS;

EID: 28244479844     PISSN: 00207160     EISSN: 10290265     Source Type: Journal    
DOI: 10.1080/0020716031000079554     Document Type: Article

References (25)

1. Bellman, R., Azen, S. P. and Richardaon, J. M. (1965). On new and direct computational approaches to some mathematical model turbulence. Quart. App. Math., 23, 55-67.
2. Taylor, G. L., Ndefo, E. and Masson, B. S. (1972). A study of numerical methods for solving viscous and inviscoused flow problems. J. Comp. Phys., 9, 99-119.
3. Gazdag, J. (1973). Numerical convective schemes based on accurate computation of space derivatives. J. Comp. Phys., 13, 100-113.
4. Rubin, J. and Graves (1975). Viscous flow solutions with a cubic spline approximation. Compute. Fluids, 3, 1-36.
5. Davies, A. M. (1977). A numerical investigation of errors arising in applying the Galerkin method of the solution of nonlinear partial differential equations. Computer Methods, Appl. Mech. Eng., 11, 350-431.
6. Gurbatov, S. N. (1977). Parametric excitation of low frequence noise waves in nonlinear medium. Soviet Physics of Acoustics, 23(2), 146-148.
7. Ciment, M., Leventhal, S. H. and Weinberg, B. C. (1978). The operator compact implicit methods for parabolic equations. J. Comp. Phys., 23, 135-166.
8. Armenjan, P. and Beauchamp, C. (1978). A finite element methods for Burgers equation in Hydrodynamics. I. J. Num. Methods Eng., 12, 415-428.
9. Nickell, R. E., Gartling, D. K. and Strang, G. (1979). Spectral decomposition in advection-diffusion analysis by finite element method. Computer Method Appl. Mech. Eng., 17, 561-580.
10. Christie, I., Griffiths, D. F., Mitchell, A. R. and Serna, J. M. (1981). Product approximation for nonlinear problems in the finite element method. IMA J. Numer. Anal., 1, 253-266.
11. Herbst, B. M., Schoombie, S. W. and Mitchell, A. R. (1982). A moving Petrov-Galerkin method for transport equation. I. J. Numer. Methods Eng., 18, 1321-1336.
12. Varolgu, E. and Finn, W. (1983). Space-time finite elements incorporating characteristics for the Burgers equation. I. J. Numer. Methods Eng., 16, 171-184.
13. Saunders, R., Caldwell, J. and Wanless, P. (1984). A Variational- iterative applied to Burgers equation. J. Numer. Anal., 4, 349-362.
14. Herbst, B. M., Schoombie, S. W., Griffiths, D. F. and Mitchell, A. R. (1984). Generalized Petrov-Galerkin methods for the numerical solution of Burgers equation. I. J. Numer. Method Eng., 20, 1273-1289.
15. Nguyen, H. and Reynen, J. (1987). A space-time finite element approach to Burgers equation. In: Hinton, E., et al. (Eds.), Numerical Methods for Nonlinear Problems, Vol. 3, pp. 718-728.
16. Caldwell, J. (1987). Application of cubic splines to the nonlinear Burgers equation. In: Hinton, E., et al. (Eds.), Numerical Methods for Nonlinear Problems, Vol. 3, pp. 253-261.
17. Maritz, M. F. and Schoombie, S. W. (1991). Exact analysis of nonlinear instability in a discrete Burgers equation. J. Comp. Phys., 97, 73-90.
18. Gardner, L. R. T. and Ali, A. H. A. (1991). A method of lines solutions for Burgers equation. J. Comp. Mech., 1555-1561.
19. Mohsen, A. and Iskandar, L. (1992). Some numerical experiments on the splitting of Burgers equation. Numer. Methods Part Differ. Equ., 8, 267-276.
20. Ali, A. H. A., Gardner, G. A. and Gardner, L. R. T. (1992). A collocation solution for Burgers equation using cubic B-spline finite elements. Computer Method Appl. Mech. Eng., 100, 325-337.
21. 2) finite difference method for one-space Burgers equation in polar coordinates. Numer. Methods Part. Differ. Equ., 12, 579-583.
22. El Danf, T. S. A. (1998). Efficient and accurate numerical methods for the Burgers and related partial differential equations. PhD thesis, Menoufia University, 1998.
23. Shamardan, A. B. and Abo Essa, Y. M. (2000). Multi-level adaptive solutions to initial value problems. Korean J. Comput. & Appl. Math., 7(1), 215-222.
24. Soliman, A. A. (2000). New numerical technique for Burgers equation based on similarity reductions. I. Conference on Applied Computational Fluid Dynamics, October 17-20, 2000, Beijing, China, pp. 559-566.
25. Raslan, K. R. (1999). Numerical methods for partial differential equations. PhD thesis, AL-Azhar University, Cairo, 1999.