Table of Contents Author Guidelines Submit a Manuscript
International Journal of Engineering Mathematics
Volume 2013, Article ID 768474, 11 pages
http://dx.doi.org/10.1155/2013/768474
Research Article

Interval Arithmetic for Nonlinear Problem Solving

Department of Materials Science and Engineering, Institute of Technology of Costa Rica, Cartago 07050, Costa Rica

Received 10 February 2013; Accepted 19 May 2013

Academic Editor: A. Nazli Gundes

Copyright © 2013 Benito A. Stradi-Granados. 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. R. B. Kearfott, Rigorous Global Search: Continuous Problem, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
  2. B. Stradi and E. Haven, “Optimal investment strategy via interval arithmetic,” International Journal of Theoretical and Applied Finance, vol. 8, no. 2, pp. 185–206, 2005. View at Publisher · View at Google Scholar · View at Scopus
  3. B. A. Stradi-Granados and E. Haven, “The use of interval arithmetic in solving a non-linear rational expectation based multiperiod output-inflation process model: the case of the IN/GB method,” European Journal of Operational Research, vol. 203, no. 1, pp. 222–229, 2010. View at Publisher · View at Google Scholar · View at Scopus
  4. B. A. Stradi, J. F. Brennecke, P. Kohn, and M. A. Stadtherr, “Reliable computation of mixture critical points,” AIChE Journal, vol. 47, no. 1, pp. 212–221, 2001. View at Publisher · View at Google Scholar · View at Scopus
  5. H. Gecegormez and Y. Demirel, “Phase stability analysis using interval Newton method with NRTL model,” Fluid Phase Equilibria, vol. 237, no. 1-2, pp. 48–58, 2005. View at Publisher · View at Google Scholar · View at Scopus
  6. Z. Galias, “Proving the existence of long periodic orbits in 1D maps using interval Newton method and backward shooting,” Topology and its Applications, vol. 124, no. 1, pp. 25–37, 2002. View at Publisher · View at Google Scholar · View at Scopus
  7. M. L. Michelsen and R. A. Heidemann, “Calculation of critical points from cubic two-constant equations of state,” AIChE Journal, vol. 27, no. 2, pp. 521–523, 1981. View at Publisher · View at Google Scholar
  8. H. Hoteit, E. Santiso, and A. Firoozabadi, “An efficient and robust algorithm for the calculation of gas-liquid critical point of multicomponent petroleum fluids,” Fluid Phase Equilibria, vol. 241, no. 1-2, pp. 186–195, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. D. V. Nichita and S. Gomez, “Efficient and reliable mixture critical points calculation by global optimization,” Fluid Phase Equilibria, vol. 291, no. 2, pp. 125–140, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. M. L. Michelsen, “Calculation of phase envelopes and critical points for multicomponent mixtures,” Fluid Phase Equilibria, vol. 4, no. 1-2, pp. 1–10, 1980. View at Google Scholar · View at Scopus
  11. M. L. Michelsen, “Phase equilibrium calculations. What is easy and what is difficult?” Computers and Chemical Engineering, vol. 17, no. 5-6, pp. 431–439, 1993. View at Google Scholar · View at Scopus
  12. M. L. Michelsen and H. Kistenmacher, “On composition-dependent interaction coefficeints,” Fluid Phase Equilibria, vol. 58, no. 1-2, pp. 229–230, 1990. View at Google Scholar · View at Scopus
  13. M. L. Michelsen and R. A. Heidemann, “Calculation of tri-critical points,” Fluid Phase Equilibria, vol. 39, no. 1, pp. 53–74, 1988. View at Google Scholar · View at Scopus
  14. M. L. Michelsen, “Calculation of critical points and phase boundaries in the critical region,” Fluid Phase Equilibria, vol. 16, no. 1, pp. 57–76, 1984. View at Google Scholar · View at Scopus
  15. J. Cai, H. Liu, Y. Hu, and J. M. Prausnitz, “Critical properties of polydisperse fluid mixtures from an equation of state,” Fluid Phase Equilibria, vol. 168, no. 1, pp. 91–106, 2000. View at Publisher · View at Google Scholar · View at Scopus
  16. T. Lindvig, L. L. Hestkjar, A. F. Hansen, M. L. Michelsen, and G. M. Kontogeorgis, “Phase equilibria for complex polymer solutions,” Fluid Phase Equilibria, vol. 194–197, pp. 663–673, 2002. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Cismondi and M. L. Michelsen, “Global phase equilibrium calculations: critical lines, critical end points and liquid-liquid-vapour equilibrium in binary mixtures,” Journal of Supercritical Fluids, vol. 39, no. 3, pp. 287–295, 2007. View at Publisher · View at Google Scholar · View at Scopus
  18. C. Carstensen and M. S. Petković, “On iteration methods without derivatives for the simultaneous determination of polynomial zeros,” Journal of Computational and Applied Mathematics, vol. 45, no. 3, pp. 251–266, 1993. View at Google Scholar · View at Scopus
  19. C. D. Maranas and C. A. Floudas, “Finding all solutions of nonlinearly constrained systems of equations,” Journal of Global Optimization, vol. 7, no. 2, pp. 143–182, 1995. View at Publisher · View at Google Scholar · View at Scopus
  20. R. B. Kearfott and M. Novoa III, “Algorithm 681 INTBIS, a portable interval Newton/bisection package,” ACM Transactions on Mathematical Software, vol. 16, no. 2, pp. 152–157, 1990. View at Publisher · View at Google Scholar · View at Scopus
  21. S. M. Rump, “INTLAB: INTerval LABoratory,” in Developments in Reliable Computing, T. Csendes, Ed., pp. 77–104, Kluwer Academic Publishers, Dodrecht, The Netherlands, 1999. View at Google Scholar
  22. “Matlab R2011b (64 bit),” Mathworks, Natick, Mass, USA, 2011.
  23. S. C. Chapra and R. P. Canale, Numerical Methods for Engineers, McGraw-Hill, New York, NY, USA, 6th edition, 2010.
  24. S. Nakamura, Numerical Analysis and Graphical Visualization, Prentice-Hall, Upper Saddle River, NJ, USA, 2nd edition, 2001.
  25. S. Attaway, MAtlab: A Practical Introduction to Programming and Problem Solving, Butterworth-Heinemann, New York, NY, USA, 2nd edition, 2011.
  26. K. Ozaki, T. Ogita, S. M. Rump, and S. Oishi, “Fast algorithms for floating-point interval matrix multiplication,” Journal of Computational and Applied Mathematics, vol. 236, no. 7, pp. 1795–1814, 2012. View at Publisher · View at Google Scholar · View at Scopus
  27. S. M. Rump and T. Ogita, “Super-fast validated solution of linear systems,” Journal of Computational and Applied Mathematics, vol. 199, no. 2, pp. 199–206, 2007. View at Publisher · View at Google Scholar · View at Scopus
  28. R. C. Reid, J. M. Prausnitz, and B. E. Poling, The Properties of Gases and Liquids, McGraw-Hill, New York, NY, USA, 4th edition, 1987.
  29. A. Neumaier, Interval Methods for Systems of Equations, Cambridge University Press, Cambridge, UK, 1990.
  30. R. Moore, Interval Analysis, Prentice-Hall, Upper Saddle River, NJ, USA, 1966.