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Original Articles

An efficient hybrid numerical scheme for convection-dominated boundary-value problems

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Pages 261-273 | Received 10 Sep 2007, Accepted 27 Jan 2008, Published online: 05 Dec 2008

References

  • Roos , H.-G. , Stynes , M. and Tobiska , L. 1996 . Numerical Methods for Singularly Perturbed Differential Equations , Berlin : Springer .
  • O'Malley , R. E. 1991 . Singular Perturbation Methods for Ordinary Differential Equations , New York : Springer .
  • Doolan , E. P. , Miller , J. J.H. and Schildres , W. H.A. 1980 . Uniform Numerical Methods for Problems with Initial and Boundary Layers , Dublin : Boole Press .
  • Miller , J. J.H. , O'Riordan , E. and Shishkin , G. I. 1996 . Fitted Numerical Methods for Singular Perturbation Problems , Singapore : World Scientific .
  • Natesan , S. and Ramanujam , N. 2002 . ‘Shooting Method’ for the solution of singularly perturbed two-point boundary-value problems having less severe boundary layers . Appl. Math. Comput. , 133 : 623 – 641 .
  • Natesan , S. , Vigo-Aguiar , J. and Ramanujam , N. 2003 . A Numerical algorithm for singular perturbation problems exhibiting weak boundary layers . Comput. Math. Appl. , 45 : 469 – 479 .
  • Vigo-Aguiar , J. and Natesan , S. 2004 . A parallel boundary value technique for singularly perturbed two-point boundary value problems . J. Supercomput. , 27 : 195 – 206 .
  • Natesan , S. and Ramanujam , N. 1999 . Booster method for singularly perturbed one-dimensional convection–diffusion Neumann problems . J. Optim. Theory Appl. , 99 : 53 – 72 .
  • Vigo-Aguiar , J. and Natesan , S. 2006 . An efficient numerical method for singular perturbation problems . J. Comp. Appl. Math. , 192 : 132 – 141 .
  • Kadalbajoo , M. K. and Bawa , R. K. 1996 . Variable mesh difference scheme for singularly perturbed boundary value problems . J. Optim. Theory Appl. , 90 : 405 – 416 .
  • Natesan , S. , Jayakumar , J. and Vigo-Aguiar , J. 2003 . Parameter uniform numerical method for singularly perturbed turning point problems exhibiting boundary layers . J. Comput. Appl. Math. , 158 : 121 – 134 .
  • Stynes , M. and Roos , H.-G. 1997 . The midpoint upwind scheme . Appl. Numer. Math. , 23 : 361 – 374 .
  • Natesan , S. and Bawa , R. K. 2008 . Second-order parameter-uniform error estimate for convection-dominated two-point boundary-value problems Working Paper
  • Farrell , P. A. , Hegarty , A. F. , Miller , J. J.H. , O'Riordan , E. and Shishkin , G. I. 2001 . Parameter-uniform numerical methods for a class of singularly perturbed problems with a Neumann boundary condition . Lect. Notes Comput. Sci. , 1988 : 292 – 303 .

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