A mixed finite difference and boundary element approach to one-dimensional Burgers' equation

Applied Mathematics and Computation

Volumn 160, Issue 3, 2005, Pages 663-673

  Bahadir, A Refik ^a   Saǧlam, Mustafa ^a  

^a INONU UNIVERSITY   (Turkey)

Author keywords

Boundary element method; Burgers' equation

Indexed keywords

KINEMATICS; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PARAMETER ESTIMATION; PROBLEM SOLVING; VISCOSITY;

ANALYTICAL SOLUTIONS; BURGER EQUATION; FINITE DIFFERENCES; NUMERICAL SOLUTIONS;

BOUNDARY ELEMENT METHOD;

EID: 9544241325     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2003.11.024     Document Type: Article

References (21)

1. J.M. Burger, A Mathematical Model Illustrating the Theory of Turbulence, Academic Press, New York, 1948.
2. J.D. Cole, On a quasilinear parabolic equations occurring in aerodynamics, Quart. Appl. Math. 9 (1951) 225-236.
3. xx, Commun. Pure Appl. Math. 3 (1950) 201-230.
4. E.L. Miller, Predictor-corrector studies of Burger's model of turbulent flow, M.Sc. thesis, University of Delaware, Newark, Delaware, 1966.
5. E. Varoǧlu, W.D.L. Finn, Space time finite elements incorporating characteristics for the Burgers' equations, Int. J. Numer. Meth. Eng. 16 (1980) 171-184.
6. J. Caldwell, P. Smith, Solution of Burger's equation with a large Reynold's number, Appl. Math. Model. 6 (1982) 381-385.
7. J. Caldwell, Numerical approaches to Burger's equation, in: C. Taylor (Ed.), Numerical Methods for Nonlinear Problems, vol. 2, Pineridge Press, 1984, pp. 700-717.
8. J. Caldwell, P. Wanless, A.E. Cook, A finite-element approach to Burger's equation, Appl. Math. Model. 5 (1981) 189-193.
9. D.J. Evans, A.R. Abdullah, The group explicit method for the solution of Burger's equation, Computing 32 (1984) 239-253.
10. H. Nguyen, J. Reynen, A space-time finite-element approach to Burger's equation, in: C. Taylor (Ed.), Numerical Methods for Non-linear Problems, vol. 2, Pineridge Press, 1982, pp. 718-728.
11. G. Adomian, Explicit solutions of nonlinear partial differential equations, Appl. Math. Comput. 88 (1997) 117-126.
12. A.R. Bahadir, Numerical solution for one-dimensional Burgers' equation using a fully implicit finite-difference method, Int. J. Appl. Math. 8 (1999) 897-909.
13. Y.C. Hon, X.Z. Mao, An efficient numerical scheme for Burgers' equation, Appl. Math. Comput. 95 (1998) 37-50.
14. R.C. Mittal, P. Singhal, Numerical solution of Burger's equation, Commun. Numer. Meth. Eng. 9 (1993) 397-406.
15. S. Kutluay, A.R. Bahadir, A. Özdeş, Numerical solution of one-dimensional Burgers equation: explicit and exact-explicit finite difference methods, J. Comput. Appl. Math. 103 (1999) 251-261.
16. C.A. Brebbia, S. Walker, The Boundary Element Techniques in Engineering, Newnes-Butterworths, London, 1980.
17. C.A. Brebbia, D. Nardini, Dynamic analysis in solid mechanics by an alternative boundary element procedure, Eng. Anal. Bound. Elem. 24 (2000) 513-518.
18. E. Chino, N. Tosaka, Dual reciprocity boundary element analysis of time-independent Burgers' equation, Research Note, Eng. Anal. Bound. Elem. 21 (1998) 261-270.
19. K. Kakuda, N. Tosaka, The generalized boundary element approach to Burgers' equation, Int. J. Numer. Meth. Eng. 29 (1990) 245-261.
20. J.M. Hill, J.N. Dewynne, Heat conduction, in: Applied Mathematics and Engineering Science Texts, Blackwell Scientific Publications, Oxford, London, 1987.
21. M. Saǧlam, Solution of the Burger's equation by the boundary element method, M.Sc. Thesis, İnönü University, Malatya, Turkey, 2002 (in Turkish).