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Miscellany

A lumped Galerkin method for solving the Burgers equation

Pages 1433-1444 | Received 18 Feb 2004, Published online: 25 Jan 2007

References

References

  • Cole , JD . (1951) . On a quasi linear parabolic equation occurring in aerodynamics . Q. Appl. Math. , 9 : 225 – 236 .
  • Varoglu E Finn WDL (1980) Space time finite elements incorporating characteristics for the Burgers’ equations Int. J. Num. Methods Eng., 16, 171 184
  • Hopf , E . (1950) . The partial differential equation Ut  + UUx  = μ Uxx . Commun. Pure Appl. Math. , 3 : 201 – 230 .
  • Benton E Platzman GW (1972) A table of solutions of the one-dimensional Burgers’ equation Q. Appl. Math., 30, 195 212
  • Miller EL (1966) Predictor–corrector studies of Burger's model of turbulent flow M.S. Thesis, University of Delaware Newark Delawar
  • Evans DJ Abdullah AR (1984) The group explicit method for the solution of Burgers’ equation Computing, 32, 239 253
  • Kutluay S Bahadir AR Özdes A (1999) Numerical solution of one-dimensional Burgers’ equation: explicit and exact-explicit finite difference methods J. Comput. Appl. Math., 103 251 261
  • Kutluay S Esen A A linearized numerical scheme for Burgers-like equations Appl. Math. Comput. (AMC 8346 in press)
  • Jamet P Bonnerot R (1975) Numerical solution of compressible flow by finite element method which follows the free boundary and the interfaces J. Comput. Phys., 18, 21 45
  • Caldwell , J , Wanless , P and Cook , E . (1981) . A finite element approach to Burgers’ equation . Appl. Math. Model. , 5 : 189 – 193 .
  • Nguyen , H and Reynen , J . (1982) . A space–time finite element approach to Burgers’ equation. In: C. Taylor et al. (Eds.) . Numerical Methods for Nonlinear Problems, Pineridge Press , 2 : pp. 718–728
  • Ali AHA Gardner GA Gardner LRT (1992) A collocation solution for Burgers’ equation using cubic B-spline finite elements Comput. Methods Appl. Mech. Eng., 100 325 337
  • Gardner LRT Gardner GA Ali AHA (1991) A method of lines solution for Burger's equation In: Cheung, Lee and Leung (Eds.) Computational Mechanics, Balkema, Rotterdam pp. 1555–1561
  • Gardner LRT Gardner GA Dogan A (1997) A Petrov–Galerkin scheme for Burgers’ equation Arab. J. Sci. Eng., 22, 99 109
  • Kutluay S Esen A Dag I (2004) Numerical solutions of the Burgers’ equation by the least-squares quadratic B-spline finite element method J. Comput. Appl. Math., 167 21 33
  • Kakuda K Tosaka N (1990) The generalised boundary element approach to Burgers’ equation Int. J. Num. Methods Eng., 29, 245 261
  • Mittal , RC and Singhal , P . (1993) . Numerical solution of Burgers’ equation . Commun. Num. Methods Eng. , 9 : 397 – 406 .
  • Özis T Özdes A (1996) A direct variational methods applied to Burgers’ equation J. Comput. Appl. Math., 71, 163 175
  • Prenter PM (1975) Splines and Variational Methods, John-Wiley New York
  • Smith GD (1987) Numerical Solution of Partial Differential Equations: Finite Difference Methods 3rd Edition Clarendon Press Oxford

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