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Section B

Implementation of parallel three-point block codes for solving large systems of ordinary differential equations

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Pages 1415-1429 | Received 14 Jan 2007, Accepted 09 Jul 2008, Published online: 28 May 2009

References

  • Burrage , K. and Suhartanto , H. 1997 . Parallel iterated methods based on multistep Runge–Kutta methods of Radau type . Adv. Comput. Math. , 7 : 37 – 57 .
  • Burrage , K. and Suhartanto , H. 1997 . Parallel iterated method on multistep Runge–Kutta of Radau type for stiff problems . Adv. Comput. Math. , 7 : 59 – 77 .
  • Burrage , K. and Suhartanto , H. 2000 . Parallel iterated methods based on variable step-size multistep Runge–Kutta methods of Radau type for stiff problems . Adv. Comput. Math. , 13 : 257 – 270 .
  • Char , B. W. , Geddes , K. O. , Gonnet , G. H. , Leong , B. L. , Monagan , M. B. and Watt , S. M. 1992 . First Leaves: A Tutorial Introduction to Maple V , VA, USA : Springer-Verlag, Waterloo Maple Publishing .
  • Cong , N. H. , Strehmel , K. , Weiner , R. and Podhaisky , H. 1999 . Runge–Kutta–Nystrom-type parallel block predictor corrector methods . Adv. in Comput. Math. , 10 : 115 – 133 .
  • Garcia , A. , Martin , P. and Gonzales , B. A. 2004 . Higher order Runge–Kutta nystrom codes for the integration of oscillatory problems . Appl. Numer. Math. , 48 : 13 – 25 .
  • Gear , C. W. 1971 . Numerical Initial Value Problems in Ordinary Differential Equations , New Jersey : Prentice Hall, Inc .
  • Hull , T. E. , Enright , W. E. , Fellel , B. M. and Sedgwick , A. E. 1972 . Comparing numerical methods for ordinary differential equations . SIAM J. Num. Anal. , 9 ( 4 ) : 603 – 637 .
  • Krogh , F. T. A variable step, variable order multistep method for the numerical solution of ordinary differential equations . Proceeding of the IFIP Congress Edinburgh in Information Processing 68 . Edited by: Morrell , A. J.H. pp. 194 – 199 .
  • Majid , Z. A. and Suleiman , M. B. 2006 . Parallel block codes for solving large systems of ordinary differential equations . Int. J. Simulation Process Model , 2 ( 1/2 ) : 98 – 112 .
  • Omar , Z. 1999 . “ Developing parallel block methods for solving higher order ODEs directly ” . Malaysia : University Putra Malaysia . Ph.D. thesis
  • Shampine , L. F. and Gordon , M. K. 1975 . “ Computer Solution of Ordinary Differential Equations: The Initial Value Problem ” . San Francisco : W.H. Freeman and company .
  • Suleiman , M. B. 1979 . “ Generalised multistep Adams and backward differentiation methods for the solution of stiff and non-stiff ordinary differential equations ” . University of Manchester . Ph.D. thesis

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