Table of Contents
Journal of Computational Engineering
Volume 2013, Article ID 720812, 5 pages
http://dx.doi.org/10.1155/2013/720812
Research Article

An Implicit Method for Numerical Solution of Singular and Stiff Initial Value Problems

Department of Mathematics, Rajshahi University of Engineering and Technology, Rajshahi 6204, Bangladesh

Received 29 April 2013; Revised 27 August 2013; Accepted 30 August 2013

Academic Editor: Fu-Yun Zhao

Copyright © 2013 M. Kamrul Hasan et al. 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. D. M. McClung and A. I. Mears, “Dry-flowing avalanche run-up and run-out,” Journal of Glaciology, vol. 41, no. 138, pp. 359–369, 1995. View at Google Scholar · View at Scopus
  2. O. Koch, P. Kofler, and E. B. Weinmüller, “The implicit Euler method for the numerical solution of singular initial value problems,” Applied Numerical Mathematics, vol. 34, no. 2-3, pp. 231–252, 2000. View at Publisher · View at Google Scholar · View at Scopus
  3. O. Koch and E. Weinmüller, “Analytical and numerical treatment of a singular initial value problem in avalanche modeling,” Applied Mathematics and Computation, vol. 148, no. 2, pp. 561–570, 2004. View at Publisher · View at Google Scholar · View at Scopus
  4. H. M. Antia, Numerical methods for scientists and engineers [M.S. thesis], McGraw-Hill, New Delhi, India, 1991.
  5. O. Y. Ababneh and R. Ahmad, “Construction of third-order diagonal implicit Runge-Kutta methods for stiff problems,” Chinese Physics Letters, vol. 26, no. 8, Article ID 080503, 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. R. Alexander, “Diagonally implicit Runge-Kutta methods for stiff O.D.E.'s,” SIAM Journal on Numerical Analysis, vol. 14, no. 6, pp. 1006–1021, 1977. View at Publisher · View at Google Scholar
  7. O. Y. Ababneh, R. Ahmad, and E. S. Ismail, “Design of new diagonally implicit Runge-Kutta methods for stiff problems,” Applied Mathematical Sciences, vol. 3, no. 45, pp. 2241–2253, 2009. View at Google Scholar · View at Scopus
  8. M. A. Huq, M. K. Hasan, M. M. Rahman, and M. S. Alam, “A simple and straightforward method for evaluating some singular integrals,” Far East Journal of Mathematical Education, vol. 7, no. 2, pp. 93–107, 2011. View at Google Scholar
  9. M. K. Hasan, M. A. Huq, M. S. Rahman, M. M. Rahman, and M. S. Alam, “A new implicit method for numerical solution of singular initial value problems,” in Proceeding of the International Conference on Mathematics and Information Technology (ICMIT-Mar '13), pp. 36–40, India, 2013.
  10. M. Ali Akbar, M. S. Alam, and M. A. Sattar, “KBM unified method for solving an n-th order non-linear differential equation under some special conditions including the case of internal resonance,” International Journal of Non-Linear Mechanics, vol. 41, no. 1, pp. 26–42, 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. M. A. Razzak, M. S. Rahman, K. C. Roy, B. M. I. Haque, and M. S. Alam, “An analytical technique to find approximate solutions of strongly nonlinear damped with forced systems,” Bulletin of Calcutta Mathematical Society, vol. 105, no. 3, 2013. View at Google Scholar