Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015, Article ID 193179, 10 pages
http://dx.doi.org/10.1155/2015/193179
Research Article

An Accurate Method for Real-Time Aircraft Dynamics Simulation Based on Predictor-Corrector Scheme

1National CIMS Engineering Research Centre, Tsinghua University, Beijing 100084, China
2State Key Laboratory of Civil Aircraft Flight Simulation, Shanghai Aircraft Design and Research Institute, Shanghai 201210, China
3School of Engineering, University of Portsmouth, Portsmouth PO1 3DJ, UK

Received 4 June 2014; Revised 15 October 2014; Accepted 28 October 2014

Academic Editor: Kang Li

Copyright © 2015 Jiaxin Zhao 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. B. L. Stevens and F. L. Lewis, Aircraft Control and Simulation, vol. 2, John Wiley & Sons, New York, NY, USA, 2003.
  2. M. T. Heath, Scientific Computing, McGraw-Hill, New York, NY, USA, 1997.
  3. Y. Xu and J. J. Zhao, “Estimation of longest stability interval for a kind of explicit linear multistep methods,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 912691, 18 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. Z. A. Majid, N. Z. Mokhtar, and M. Suleiman, “Direct two-point block one-step method for solving general second-order ordinary differential equations,” Mathematical Problems in Engineering, vol. 2012, Article ID 184253, 16 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  5. G. G. Dahlquist, “A special stability problem for linear multistep methods,” BIT Numerical Mathematics, vol. 3, pp. 27–43, 1963. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. L. F. Shampine and C. W. Gear, “A user's view of solving stiff ordinary differential equations,” SIAM Review, vol. 21, no. 1, pp. 1–17, 1979. View at Publisher · View at Google Scholar · View at MathSciNet
  7. H. H. Rosenbrock, “Some general implicit processes for the numerical solution of differential equations,” The Computer Journal, vol. 5, no. 4, pp. 329–330, 1963. View at Google Scholar · View at MathSciNet
  8. C. Huang, “Strong stability preserving hybrid methods,” Applied Numerical Mathematics, vol. 59, no. 5, pp. 891–904, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. S. Gottlieb, C.-W. Shu, and E. Tadmor, “Strong stability-preserving high-order time discretization methods,” SIAM Review, vol. 43, no. 1, pp. 89–112, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. M. V. Bulatov and G. V. Berghe, “Two-step fourth order methods for linear ODEs of the second order,” Numerical Algorithms, vol. 51, no. 4, pp. 449–460, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. C. Bresten, S. Gottlieb, Z. Grant, D. Higgs, D. I. Ketcheson, and Németh, “Strong stability preserving multistep Runge-Kutta methods,” http://arxiv.org/abs/1307.8058.
  12. H. Y. Seong, Z. A. Majid, and F. Ismail, “Solving second-order delay differential equations by direct Adams-Moulton method,” Mathematical Problems in Engineering, vol. 2013, Article ID 261240, 7 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  13. H. Wang, H. Mao, and H. Zhang, “A variable-step interaction algorithm for multidisciplinary collaborative simulation,” Integrated Computer-Aided Engineering, vol. 21, no. 3, pp. 263–279, 2014. View at Google Scholar
  14. F. Bergero and E. Kofman, “PowerDEVS: a tool for hybrid system modeling and real-time simulation,” Simulation, vol. 87, no. 1-2, pp. 113–132, 2011. View at Publisher · View at Google Scholar · View at Scopus
  15. X. Wang, J. Zhang, and M. Scalia, “Parallel motion simulation of large-scale real-time crowd in a hierarchical environmental model,” Mathematical Problems in Engineering, vol. 2012, Article ID 918497, 15 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  16. O. B. Widlund, “A note on unconditionally stable linear multistep methods,” BIT Numerical Mathematics, vol. 7, pp. 65–70, 1967. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. K. E. Atkinson, An Introduction to Numerical Analysis, John Wiley & Sons, New York, NY, USA, 2008. View at MathSciNet
  18. Q. Y. Li, Z. Guan, and F. S. Bai, Numerical Calculation Principle, Tsinghua University Press, Beijing, China, 2000.
  19. T. E. Hull, W. H. Enright, B. M. Fellen, and A. E. Sedgwick, “Comparing numerical methods for ordinary differential equations,” SIAM Journal on Numerical Analysis, vol. 9, no. 4, pp. 603–637, 1972. View at Publisher · View at Google Scholar · View at Scopus
  20. H. M. Zhang, S. Liang, S. J. Song, and H. W. Wang, “Truncation error calculation based on Richardson extrapolation for variable-step collaborative simulation,” Science China Information Sciences, vol. 54, no. 6, pp. 1238–1250, 2011. View at Publisher · View at Google Scholar · View at Scopus
  21. G. Zoutendijk, Methods of Feasible Directions; A Study in Linear and Nonlinear Programming, Elsevier, New York, NY, USA, 1960.
  22. M. Frank and P. Wolfe, “An algorithm for quadratic programming,” Naval Research Logistics Quarterly, vol. 3, no. 1, pp. 95–110, 1956. View at Publisher · View at Google Scholar · View at MathSciNet
  23. C. R. Houck, J. Joines, and M. Kay, “GA genetic algorithm for function optimization: a Matlab implementation,” NCSU-IE TR, 1995.
  24. O. Kramer and H.-P. Schwefel, “On three new approaches to handle constraints within evolution strategies,” Natural Computing, vol. 5, no. 4, pp. 363–385, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  25. F. Zong, H. Lin, B. Yu, and X. Pan, “Daily commute time prediction based on genetic algorithm,” Mathematical Problems in Engineering, vol. 2012, Article ID 321574, 20 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  26. C. Coello and C. Artemio, “Constraint-handling techniques used with evolutionary algorithms,” in Proceedings of the 14th International Conference on Genetic and Evolutionary Computation Conference Companion, ACM, 2012.
  27. J. S. Litt, D. L. Simon, S. Garg et al., “A survey of intelligent control and health management technologies for aircraft propulsion systems,” Journal of Aerospace Computing, Information and Communication, vol. 1, no. 12, pp. 543–563, 2004. View at Google Scholar · View at Scopus
  28. L. Stevens, Aircraft Control and Simulation, John Wiley & Sons, 1992.
  29. R. S. Russel, “Nonlinear f-16 simulation using Simulink and matlab,” Tech. Rep., University of Minnesota, 2003. View at Google Scholar
  30. J. A. Mulder, W. H. J. J. van Staveren, and J. C. van der Vaart, “Flight dynamics,” Tech. Rep., Delft University of Technology, 2000. View at Google Scholar