Table of Contents
International Journal of Computational Mathematics
Volume 2014 (2014), Article ID 162103, 8 pages
http://dx.doi.org/10.1155/2014/162103
Research Article

Block Hybrid -Step Backward Differentiation Formulas for Large Stiff Systems

1Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044, USA
2School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623-5603, USA

Received 16 June 2014; Revised 29 September 2014; Accepted 30 September 2014; Published 20 October 2014

Academic Editor: Zhijie Xu

Copyright © 2014 S. N. Jator and E. Agyingi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. W. Jackson and S. K. Kenue, “A fourth order exponentially fitted method,” SIAM Journal on Numerical Analysis, vol. 11, pp. 965–978, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. J. R. Cash, “Two new finite difference schemes for parabolic equations,” SIAM Journal on Numerical Analysis, vol. 21, no. 3, pp. 433–446, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. W. H. Enright, “Continuous numerical methods for ODEs with defect control,” Journal of Computational and Applied Mathematics, vol. 125, no. 1-2, pp. 159–170, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. P. Onumanyi, U. W. Sirisena, and S. N. Jator, “Continuous finite difference approximations for solving differential equations,” International Journal of Computer Mathematics, vol. 72, no. 1, pp. 15–27, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. P. Onumanyi, D. O. Awoyemi, S. N. Jator, and U. W. Sirisena, “New linear multistep methods with continuous coefficients for first order initial value problems,” Journal of the Nigerian Mathematical Society, vol. 13, pp. 37–51, 1994. View at Google Scholar · View at MathSciNet
  6. O. A. Akinfenwa, S. N. Jator, and N. M. Yao, “Continuous block backward differentiation formula for solving stiff ordinary differential equations,” Computers & Mathematics with Applications, vol. 65, no. 7, pp. 996–1005, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. S. N. Jator, “On the hybrid method with three off-step points for initial value problems,” International Journal of Mathematical Education in Science and Technology, vol. 41, no. 1, pp. 110–118, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. L. F. Shampine and H. A. Watts, “Block implicit one-step methods,” Mathematics of Computation, vol. 23, pp. 731–740, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. P. Chartier, “L-stable parallel one-block methods for ordinary differential equations,” SIAM Journal on Numerical Analysis, vol. 31, no. 2, pp. 552–571, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. J. D. Rosser, “A Runge-kutta for all seasons,” SIAM Review, vol. 9, pp. 417–452, 1967. View at Publisher · View at Google Scholar · View at MathSciNet
  11. M. T. Chu and H. Hamilton, “Parallel solution of ODE's by multi-block methods,” SIAM Journal on Scientific and Statistical Computing, vol. 8, no. 3, pp. 342–353, 1987. View at Publisher · View at Google Scholar
  12. S. N. Jator, S. Swindell, and R. French, “Trigonometrically fitted block Numerov type method for y=fx,y,y,” Numerical Algorithms, vol. 62, no. 1, pp. 13–26, 2013. View at Publisher · View at Google Scholar · View at Scopus
  13. S. N. Jator, “Leaping type algorithms for parabolic partial differential equations,” in International Conference on Scientific Computing, Abuja, Nigeria, August 2011.
  14. L. Brugnano and D. Trigiante, Solving Differential Problems by Multistep Initial and Boundary Value Methods, Gordon and Breach Science Publishers, Amsterdam, Netherlands, 1998. View at MathSciNet
  15. S. O. Fatunla, “Block methods for second order IVPs,” International Journal of Computer Mathematics, vol. 41, pp. 55–63, 1991. View at Google Scholar
  16. P. Henrici, Discrete Variable Methods in ODEs, John Wiley & Sons, 1962. View at MathSciNet
  17. P. Amodio and F. Mazzia, “Boundary value methods based on Adams-type methods,” Applied Numerical Mathematics, vol. 18, no. 1–3, pp. 23–35, 1995. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. J. M. Vaquero and J. Vigo-Aguiar, “Exponential fitted Runge-Kutta methods of collocation type based on Gauss, Radau, and Labatto traditional methods,” in Proceedings of the International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE '07), pp. 289–303, 2007.
  19. R. Jeltsch, “Multistep methods using higher derivatives and damping at infinity,” Mathematics of Computation, vol. 31, no. 137, pp. 124–138, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. J. D. Lambert, Numerical Methods for Ordinary Differential Systems, John Wiley & Sons, New York, NY, USA, 1991. View at MathSciNet
  21. H. Ramos and J. Vigo-Aguiar, “A fourth-order runge-kutta method based on BDF-type chebyshev approximations,” Journal of Computational and Applied Mathematics, vol. 204, no. 1, pp. 124–136, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus