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Original Articles

Parallel-Iterated RK-Type PC Methods With Continuous Output Formulas * This work was partly supported by N.R.P.F.S.

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Pages 1025-1035 | Published online: 15 Sep 2010

  • Burrage , K. 1993 . Efficient block predictor-corrector methods with a small number of corrections . J. Comput. Appl. Math. , 45 : 139 – 150 .
  • Burrage , K. 1993 . Parallel methods for initial value problems . Appl Numer. Math. , 11 : 5 – 25 .
  • Burrage , K. 1995 . Parallel and Sequential Methods for Ordinary Differential Equations , Oxford : Clarendon Press .
  • Burrage , K. and Suhattanto , H. 1997 . Parallel iterated methods based on multistep Runge-Kutta mehods of Radau type . Advances in Computational Mathematics , 7 : 37 – 57 .
  • Butcher , J. C. 1987 . The Numerical Analysis of Ordinary Differential Equations, Runge-Kutta and General Linear Methods , New York : Wiley .
  • Cong , N. H. 1994 . Parallel iteration of symmetric Runge-Kutta for nonstiff initial-value problems . J. Comput. Appl. Math. , 51 : 117 – 125 .
  • Cong , N. H. 1999 . Explicit pseudo two-step Runge-Kutta methods for parallel computers . Intern. J. Comput. Math. , 73 : 77 – 91 .
  • Cong , N. H. 1999 . Continuous variable stepsize explicit pseudo two-step . RK methods. , 101 : 105 – 116 .
  • Cong , N. H. and Mitsui , T. 1997 . A class of explicit parallel two-step Runge-Kutta methods . Japan. J. Indust. Appl. Math. , 14 : 303 – 313 .
  • Cong N. H. and Mitsui, T. Parallel PC iteration of pseudo two-step RK methods for nonstiff IVPs (submitted for publication}.
  • Cong , N. H. , Podhaisky , H. and Weiner , R. 1998 . Numerical experiments with some explicit pseudo two-step RK methods on a shared memory computer . Comput. Math. Appl. , 36 : 107 – 116 .
  • Cong , N. H. and Vi , H. T. 1995 . An improvement for explicit parallel Runge-Kutta methods . Vietnam J. Math. , 23 : 241 – 252 .
  • Curtis , A. R. 1975 . High-order explicit Runge-Kutta formulae, their uses and limitations . J. Inst. Math. Appl. , 16 : 35 – 55 .
  • Curtis , A. R. 1964 . Tables of Jacobian Elliptic Functions Whose Arguments are Rational Fractions of the Quater Period , London : H.M.S.O. .
  • Hairer , E. 1978 . A Runge-Kutta method of order 10 . J. Inst. Math. Appl , 21 : 47 – 59 .
  • Hairer , E. , Nørsett , S. F. and Weiner , G. 1993 . Solving Ordinary Differential Equations, I. Nonstiff Problems , 2nd ed. , Berlin : Springer-Verlag .
  • Van Der Houwen , P. J. and Cong , N. H. 1993 . Parallel block predictor-corrector methods of Runge-Kutta type . Appl Numer. Math. , 13 : 109 – 123 .
  • Van Der Houwen , P. J. and Sommeijer , B. P. 1990 . Parallel iteration of high-order Runge-Kutta methods with stepsize control . J. Comput. Appl. Math. , 29 : 111 – 127 .
  • Van Der Houwen , P. J. and Sommeijer , B. P. 1992 . Block Runge-Kutta methods on parallel computers . Z Angew. Math. Mech. , 68 : 3 – 10 .
  • Hull , T. E. , Enright , W. H. , Fellen , B. M. and Sedgwick , A. E. 1972 . Comparing numerical methods for ordinary differential equations . SIAMJ. Numer. Anal , 9 : 603 – 637 .

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