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Section B

Convergence analysis of the Hopmoc method

Pages 1375-1393 | Received 14 May 2007, Accepted 07 Dec 2007, Published online: 17 Jun 2009

References

  • Cabral , F. L. 2001 . “ Hopmoc methods to solve convection–diffusion equations and its parallel implementation ” . In Dissertation , Instituto de Computação/Universidade Federal Fluminense . (in Portuguese)
  • Celia , M. A. 1990 . An Eulerian–Lagrangian localized adjoint method for the advection–diffusion equation . Adv. Water Res. , 13 : 187 – 206 .
  • Cuminato , J. A. and Meneguette Jr , M. 2002 . Discretization of partial differential equations: finite difference techniques . (in Portuguese) Available at http://www.lcad.icmc.usp.br/projetos/siae98/livro-poti/poti.pdf, USP São Paulo
  • Douglas , J. Jr. 1955 . On the numerical integration of u xx + u yy = u t by implicit methods . J. Soc. Ind. Appl. Math. , 3 : 42 – 65 .
  • Douglas , J. Jr. 1961 . On the numerical integration of u xx + u yy = u t Alternating direction iteration for midlly nonlinear elliptic difference equations . Numer. Math. , 3 : 92 – 98 .
  • Douglas , J. Jr. 1962 . On the numerical integration of u xx + u yy = u t Alternating direction methods for three space variables . Numer. Math. , 4 : 41 – 63 .
  • Douglas , J. Jr. 1964 . On the numerical integration of u xx + u yy = u t A general formulation of alternating direction methods . Numer. Math. , 6 : 428 – 453 .
  • Douglas , J. Jr. 1982 . On the numerical integration of u xx + u yy = u t Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures . SIAM J. Numer. Anal. , 19 : 871 – 885 .
  • Douglas , J. Jr. and Peaceman , D. 1955 . Numerical solution of two-dimensional heat flow problems . AIChE. J , 1 : 505 – 512 .
  • Duffy , D. G. 1990 . Unsteady viscous flow around a circular cylinder found by Hopscotch scheme on a vector processing machine . Appl. Numer. Math. , 6 : 195 – 208 .
  • Gordon , P. 1965 . Nonsymmetric difference equations . SIAM J. Appl. Math. , 13 : 667 – 673 .
  • Gourlay , A. R. 1970 . Hopscotch: a fast second order partial differential equation solver . J. Inst. Math. Appl. , 6 : 375 – 390 .
  • Gregory , R. T. and Karney , D. L. 1969 . A Collection of matrices for Testing Computational Algorithms , New York : Wiley-Interscience .
  • Hundsdorfer , W. H. and Verwer , J. G. 1989 . Linear stability of the Hopscotch scheme . Appl. Numer. Math. , 5 : 423 – 433 .
  • Kischinhevsky , M. An operator splitting for optimal message-passing computation of parabolic equation with hyperbolic dominance . SIAM . Missouri. Annual Meeting Kansas City ,
  • Kischinhevsky , M. 1999 . A spatially decoupled alternating direction procedure for convection–diffusion equations . Proceedings of the XXth CILAMCE-Iberian Latin American Congress on Numerical Methods in Engineearing ,
  • Oliveira , S. R.F. 2005 . “ Convergence analysis of Hopmoc methods for a convection–diffusion equation ” . In Dissertation , Instituto de Computação/Universidade Federal Fluminense . (in Portuguese)
  • Oliveira , S. R.F. and Kischinhevsky , M. 2004 . “ Consistency analysis of the odd–even Hopscotch method ” . In Seminário Brasileiro de Análise , IME/UERJ . (in Portuguese), 60o
  • Peaceman , D. W. and Rachford , H. H. 1955 . The numerical solution of parabolic and elliptic equations . J. Soc. Ind. Appl. Math. , 3 : 28 – 41 .
  • Richtmyer , R. D. and Morton , K. W. 1967 . “ Difference Methods for Initial-Value Problems ” . In Interscience New York

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