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Original Articles

Error function scheme for Burgers' equation

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Pages 371-381 | Received 01 Mar 2005, Accepted 19 Jul 2006, Published online: 25 Jan 2007

References

  • Cole , J. D. 1951 . On a quasilinear parabolic equation occurring in aerodynamics . Quarterly of Applied Mathematics , 9 : 225 – 236 .
  • Burgers , J. 1948 . A mathematical model illustrating the theory of turbulence . Advances is Applied Mechanics , : 171 – 199 .
  • Hopf , E. 1950 . The partial differential equation u t +u u x =u xx . Communications on Pure and Applied Mathematics , 3 : 201 – 230 .
  • Caldwell , J. , Wanless , P. and Cook , A. E. 1981 . A finite element approach to Burgers' equation . Applied Mathematical Modelling , 5 : 189 – 193 .
  • Herbst , B. M. , Schoombie , S. W. and Mitchell , A. R. 1982 . A moving Petrov–Galerkin for transport equations . International Journal of Numerical Methods in Engineering , 18 : 1321 – 1336 .
  • Christie , I. , Griffiths , D. F. , Mitchell , A. R. and Sanz-Serna , J. M. 1981 . Product approximation for nonlinear problems in the finite element methods . IMA Journal of Numerical Analysis , 1 : 253 – 266 .
  • Rubin , S. G. and Graves , R. A. 1975 . Viscous flow solutions with a cubic spline approximation . Computers and Fluids , 3 : 1 – 36 .
  • Caldwell , J. 1987 . Numerical Methods for Nonlinear Problems , Edited by: Hinton , E. Swansea : Pineridge .
  • Gardner , G. A. , Ali , A. H.A. and Gardner , L. R.T. 1989 . ISNME-89 , Edited by: Shaw , R. P. Berlin : Springer .
  • Ali , A. H.A. , Gardner , G. A. and Gardner , L. R.T. 1992 . A collocation solution for Burger's equation using cubic B-spline finite element . Computational Methods in Applied Mechanics and Engineering , 100 : 325 – 337 .
  • Fletcher , C. J. 1983 . A comparison of finite element and finite difference solutions of the one- and two-dimensional Burgers' equations . Journal of Computational Physics , 51 : 159
  • Radwan , S. F. 2005 . Comparison of higher-order accurate schemes for solving the two-dimensional unsteady Burgers' equation . Journal of Computational and Applied Mathematics , 174 : 383 – 397 .
  • Soliman , A. A. Paper presented at the International Conference on Computational Fluid Dynamics . October 17–20 , Beijing, China.
  • Soliman , A. A. 2004 . Numerical scheme based on similarity reductions for the regularized long wave equation . International Journal of Computer Mathematics , 81 : 1281 – 1288 .
  • Clarkson , P. A. and Kruskol , M. D. 1989 . New similarity reductions of the Boussinesq equation . Journal of Mathematical Physics , 30 : 2201 – 2213 .
  • Nguyen , H. and Reynen , J. 1987 . Numerical Methods for Nonlinear Problems , Edited by: Hinton , E. Prineridge Press .

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