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International Journal of Computer Mathematics Volume 87, 2010 - Issue 3
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Section B

Derivation of a new block method similar to the block trapezoidal rule for the numerical solution of first-order IVPs

Salman H. Abbas Department of Mathematics, College of Science, University of Bahrain, Kingdom of BahrainCorrespondence[email protected]
Pages 705-714 | Received 27 Aug 2007, Accepted 11 Apr 2008, Published online: 01 Oct 2008

References

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  • Abbas , S. 2006 . Fourth-order block methods for the numerical solution of first Order IVP's . Sarajevo J. Math. , 2 : 1 – 12 .
  • Abbas , S. 2007 . A large parallel block predictor-corrector method for initial value problems . To appear in Chaos Solutions and Fractals, Available on line , 23 January
  • Abbas , S. and Delves , L. M. 1989 . Parallel solution of ODE's by one step block methods , University of Liverpool . Report CSMR
  • Birta , L. G. and Abou-Rabia , O. 1987 . Parallel block predictor – corrector methods for ODEs . IEEE Trans. Comput. , C-36 : 299 – 311 . IEEE Trans. Comput. 8 (1991), . 201–216
  • Burrage , K. 1993 . Efficient block predictor-corrector methods with a small number of corrections . J. Comput. Appl. Math. , 45 : 139 – 150 .
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  • Franklin , M. A. 1987 . Parallel solution of ordinary differential equations . IEEE Trans. Comput. , C-27 : 413 – 420 .
  • Gear , C. W. 1987 . Parallel methods for ODEs , University of Illinois at Urbana-Champaign . Tech. Rep. UIUC-DCS-R-87-USA, Computer Science Department
  • Osterhaug , A. 1989 . Guide to Parallel Programming on Sequent Computer Systems , Prentice-Hall, Inc .
  • Shampine , L. F. and Watts , H. A. 1969 . Block implicit one-step methods . Math. Comput. , 23 : 731 – 740 .
  • Voss , D. A. and Abbas , S. 1997 . Block predictor-corrector schemes for the parallel solution of ODEs . Comput. Math. Appl. , 3 : 65 – 72 .
  • Worland , P. B. 1976 . Parallel methods for the numerical solution of ordinary differential equations . IEEE Trans. Comput. , C-25 : 1045 – 1048 .
  • Watts , H. A. and Shampine , L. F. 1972 . A-stable block implicit one-step methods . BIT , 12 : 252 – 266 .

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