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Miscellany

Implicit Runge–Kutta methods based on Lobatto quadrature formula

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Pages 77-88 | Received 28 May 2004, Published online: 25 Jan 2007

References

References

  • Butcher , JC . 1964 . Mathematical Computing , 18 : 50 – 64 .
  • Jay , LO . 1998 . SIAM Journal on Scientific Computing , 20 ( 2 ) : 416 – 446 .
  • Ehle BL 1969 On Pade Approximations to the Exponential Functions and A-stable Methods for the Numerical Solutions of Initial Value Problems Research Report CSRR 2010, Dept. AACS, University of Waterloo Ontario
  • Chipman , FH . 1971 . Birth Issue in Perinatal Care , 11 : 384 – 388 .
  • Axelsson , O . 1972 . Birth Issue in Perinatal Care , 12 : 1 – 4 .
  • Hairer , E and Wanner , G . 1981 . SIAM Journal on Numerical Analysis , 18 : 1098 – 1108 .
  • Hairer , E and Wanner , G . 1982 . Lecture Notes in Mathematics , 968 : 207 – 219 .
  • Chan , RPK . 1990 . Computing , 45 : 301 – 309 .
  • Nøsett , SP and Wanner , G . 1981 . Numerical Mathematics , 38 : 193 – 208 .
  • Geng , Sun . 1993 . Journal of Computer Mathematics , 11 : 250 – 260 .
  • Geng , Sun . 1993 . Journal of Computer Mathematics , 11 : 365 – 372 .
  • Ascher UM 1985 In: U. M. Ascher and R. D. Russel, (eds.), Numerical Boundary Values ODEs Proceedings of an International Workshop Vancouver Canada 10–13, July 1984, Progress in Scientific Computing 5, Birkhäuser Boston pp. 173–191
  • Ascher UM Mattheu RMM Russel RD 1988 Numerical Solution of Boundary Value Problems for Ordinary Differential Equations Englewood Cliffs NJ Prentice-Hall
  • Jay LO Petzold LR 1995 Highly Oscillatory Systems and Periodic-Stability AHPCRC 95-015, AHPCRC, University of Minnesota Minneapolis MN
  • Hairer E Wanner G 1991 Stiff and Differential-Algebraic Problems Berlin Springer-Verlag
  • Hairer E Lubich C Wanner G 2002 Structure-Preserving Algorithms for Ordinary Differential Equations Berlin Springer-Verlag
  • Hong JL Liu HY Sun G 2002 The multi-symplecticity of partitioned Runge–Kutta methods for Hamiltonian PDEs preprint
  • Jay , LO . 1993 . Birth Issue in Perinatal Care , 33 : 137 – 150 .
  • Jay , LO . 1996 . SIAM Journal on Numerical Analysis , 33 ( 1 ) : 368 – 387 .
  • Butcher J 1987 The numerical analysis of ODEs: RK and General Linear Methods New York Wiley
  • Chan , RPK and Chartier , P . 2003 . New Zealand Journal of Mathematics , 29 : 151 – 167 .

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