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International Journal of Computer Mathematics Volume 98, 2021 - Issue 12
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Research Article

Collocation Runge–Kutta–Nyström methods for solving second-order initial value problems

N. S. HoangDepartment of Mathematics, University of West Georgia, Carrollton, GA, USACorrespondence[email protected]
Pages 2423-2444 | Received 10 Jul 2020, Accepted 22 Feb 2021, Published online: 19 Mar 2021

References

  • K. Burrage, Parallel and Sequential Methods for Ordinary Differential Equations, Oxford University Press, Oxford, 1995.
  • J.C. Butcher, Numerical Methods for Ordinary Differential Equations, 3rd ed., Wiley, 2016. https://onlinelibrary.wiley.com/doi/book/https://doi.org/10.1002/9781119121534
  • J.P. Coleman and S.C. Duxbury, Mixed collocation methods for y″=f(t,y), J. Comput. Appl. Math. 126 (2000), pp. 47–75.
  • G.J. Cooper and A. Sayfy, Semi-explicit A-Stable Runge–Kutta Methods, Math. Comput. 33(146) (1979), pp. 541–556.
  • N.H. Cong, A-stable diagonally implicit Runge–Kutta–Nyström methods for parallel computers, Numer. Algorithms 4 (1993), pp. 263–281.
  • N.H. Cong, Note on the performance of direct and indirect Runge–Kutta–Nyström methods, J. Comput. Appl. Math. 45 (1993), pp. 347–355.
  • N.H. Cong, Explicit pseudo two-step Runge–Kutta methods for parallel computers, Int. J.Comput. Math. 73 (1999), pp. 77–91.
  • N.H. Cong, H. Podhaisky, and R. Weiner, Numerical experiments with some explicit pseudotwo-step RK methods on a shared memory computer, Math. Appl. 36(2) (1998), pp. 107–116.
  • N.H. Cong and N.V. Minh, Continuous parallel-iterated RKN-type PC methods for nonstiff IVPs, Appl. Numer. Math. 57 (2007), pp. 1097–1107.
  • E. Hairer, S.P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems, Springer, Berlin, 1987.
  • E. Hairer and G. Wanner, Solving Ordinary Differential Equations II, Stiff and Differential-algebraic Problems, Springer, Berlin, 1991.
  • L. Kramarz, Stability of collocation methods for the numerical solution of y″=f(x,y), BIT Numer. Math. 20 (1980), pp. 215–222.
  • J.D. Lambert, Numerical Methods for Ordinary Differential Systems, Wiley, Chichester, 1991.
  • L.N. Trefethen, Spectral Methods in MATLAB, Software, Environments, and Tools, Vol. 10, SIAM, Philadelphia, PA, 2000.
  • P.J. van der Houwen, B.P. Sommeijer, and N.H. Cong, Stability of collocation-based Runge–Kutta–Nyström methods, BIT Numer. Math. 31(3) (1991), pp. 469–481.
  • J. Vigo-Aguiar and H. Ramos, Variable stepsize implementation of multistep methods for y″=f(x,y,y′), J. Comput. Appl. Math. 192 (2006), pp. 114–131.

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