Fourth-order finite difference method for solving Burgers' equation

Applied Mathematics and Computation

Volumn 170, Issue 2, 2005, Pages 781-800

  Hassanien, I A ^a   Salama, A A ^a   Hosham, H A ^b  

^a Assiut University   (Egypt)

^b Assiut Branch   (Egypt)

Author keywords

Burgers' equation; Convergence; Finite difference method; Stability

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; NONLINEAR EQUATIONS; PROBLEM SOLVING; STABILITY;

BURGERS' EQUATION; CONVERGENCE; FOURTH-ORDER FINITE DIFFERENCE METHOD; UPPER BOUND;

FINITE DIFFERENCE METHOD;

EID: 27144455801     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.12.052     Document Type: Article

References (26)

1. H. Bateman Some recent researches on the motion of fluids Mon. Weather Rev. 43 1915 163 170
2. J.M. Burgers Mathematical examples illustrating relations occurring in the theory of turbulent fluid motion Trans. Roy. Neth. Acad. Sci. Amsterdam 17 1939 1 53
3. J.M. Burgers A mathematical model illustrating the theory of turbulence Adv. in Appl. Mech. vol. I 1948 Academic Press New York 171 199
4. J.D. Cole On a quasi-linear parabolic equations occuring in aerodynamics Quart. Appl. Math. 9 1951 225 236
5. xx Commun. Pure Appl. Math. 3 1950 201 230
6. E. Benton, and G.W. Platzman A table of solutions of the one-dimensional Burgers equations Quart. Appl. Math. 30 1972 195 212
7. C.A. Fletcher Burgers' equation: a model for all reasons J. Noye Numerical Solutions of Partial Differential Equations 1982 North-Holland Amsterdam 139 225
8. W.F. Ames Nonlinear Partial Differential Equations in Engineering 1965 Academic Press New York
9. İ. Daǧ, D. Irk, and B. Saka A numerical solution of the Burgers' equation using cubic B-splines Appl. Math. Comput. 163 2005 199 211
10. S. Kutluay, and A. Esen A linearized numerical scheme for Burgers-like equations Appl. Math. Comput. 156 2004 295 305
11. S. Kutluay, A. Esen, and İ. Daǧ Numerical solutions of the Burgers' equation by the least-squares quadratic B-spline finite element method J. Comput. Appl. Math. 167 2004 21 33
12. R.C. Mittal, and P. Singhal Numerical solution of Burgers' equation Commun. Numer. Meth. Eng. 9 1993 397 406
13. R.C. Mittal, and P. Singhal Numerical solution of periodic Burgers' equation Indian J. Pure Appl. Math. 27 1996 689 700
14. T. Öziş, and A. Özdeş A direct variational methods applied to Burgers' equation J. Comput. Appl. Math. 71 1996 163 175
15. A.E. Berger, J.M. Solomon, M. Ciment, S.H. Leventhal, and B.C. Weinberg Generalized OCI schemes for boundary layer problems Math. Comput. 35 1980 695 731
16. G.D. Smith Numerical Solution of Partial Differential Equations second ed. 1978 Oxford University Press Oxford
17. C. Fröberg Introduction to Numerical Analysis second ed. 1969 Addison-Wesley New York
18. R.A. Usmani, and M.J. Marsden Numerical solution of some ordinary differential equations occurring in plate deflection theory J. Eng. Math. 9 1975 1 10
19. E.N. Aksan, and A. Özdes A numerical solution of Burgers' equation Appl. Math. Comput. 156 2004 395 402
20. J. Caldwell, P. Wanless, and A.E. Cook Solution of Burgers' equation for large Reynolds number using finite elements with moving nodes Appl. Math. Model. 11 1987 211 214
21. Y.C. Hon, and X.Z. Mao An efficient numerical scheme for Burgers' equation Appl. Math. Comput. 95 1998 37 50
22. L. Iskander, and A. Mohsen Some numerical experiments on the splitting of Burgers' equation Numer. Meth. Partial Differen. Equat. 8 1992 267 276
23. S. Kutluay, A.R. Bahadir, and A. Özdeş Numerical solution of one-dimensional Burgers equation: explicit and exact-explicit finite difference methods J. Comput. Appl. Math. 103 1999 251 261
24. T. Özis, E.N. Aksan, and A. Özdes A finite element approach for solution of Burgers' equation Appl. Math. Comput. 139 2003 417 428
25. A.H.A. Ali, G.A. Gardner, and L.R.T. Gardner A collocation solution for Burgers' equation using cubic B-spline finite elements Comput. Meth. Appl. Mech. Eng. 100 1992 325 337
26. A. Dogan A Galerkin finite element approach to Burgers' equation Appl. Math. Comput. 157 2004 331 346