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Journal of Applied Mathematics
Volume 2013, Article ID 987905, 8 pages
http://dx.doi.org/10.1155/2013/987905
Research Article

Solving Nonlinear Differential Algebraic Equations by an Implicit Lie-Group Method

Department of Civil Engineering, National Taiwan University, Taipei, Taiwan

Received 26 February 2013; Accepted 28 June 2013

Academic Editor: Alexander Timokha

Copyright © 2013 Chein-Shan Liu. 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.

Citations to this Article [11 citations]

The following is the list of published articles that have cited the current article.

  • Chein-Shan Liu, “On-line detecting heat source of a nonlinear heat conduction equation by a differential algebraic equation method,” International Journal of Heat and Mass Transfer, vol. 76, pp. 153–161, 2014. View at Publisher · View at Google Scholar
  • Chein-Shan Liu, “A new sliding control strategy for nonlinear system solved by the Lie-group differential algebraic equation method,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 6, pp. 2012–2038, 2014. View at Publisher · View at Google Scholar
  • Chein-Shan Liu, “Finding unknown heat source in a nonlinear Cauchy problem by the Lie-group differential algebraic equations method,” Engineering Analysis with Boundary Elements, vol. 50, pp. 148–156, 2014. View at Publisher · View at Google Scholar
  • Chein-Shan Liu, “Lie-group differential algebraic equations method to recover heat source in a Cauchy problem with analytic continuation data,” International Journal of Heat and Mass Transfer, vol. 78, pp. 538–547, 2014. View at Publisher · View at Google Scholar
  • Chein-Shan Liu, and Satya N. Atluri, “Analysis of elastic-plastic waves in a thin-walled tube by a novel lie-group differential algebraic equations method,” Computers, Materials and Continua, vol. 41, no. 1, pp. 1–36, 2014. View at Publisher · View at Google Scholar
  • Chein-Shan Liu, “An LGDAE method to solve nonlinear cauchy problem without initial temperature,” CMES - Computer Modeling in Engineering and Sciences, vol. 99, no. 5, pp. 371–391, 2014. View at Publisher · View at Google Scholar
  • Chein-Shan Liu, “Elastoplastic models and oscillators solved by a Lie-group differential algebraic equations method,” International Journal Of Non-Linear Mechanics, vol. 69, pp. 93–108, 2015. View at Publisher · View at Google Scholar
  • Chein-Shan Liu, Chung-Lun Kuo, and Jiang-Ren Chang, “Recovering A Heat Source and Initial Value by a Lie-Group Differential Algebraic Equations Method,” Numerical Heat Transfer Part B-Fundamentals, vol. 67, no. 3, pp. 231–254, 2015. View at Publisher · View at Google Scholar
  • Xiaolin Qin, Juan Tang, Yong Feng, Bernhard Bachmann, and Peter Fritzson, “Efficient index reduction algorithm for large scale systems of differential algebraic equations,” Applied Mathematics and Computation, vol. 277, pp. 10–22, 2016. View at Publisher · View at Google Scholar
  • Chein-Shan Liu, and Chih-Wen Chang, “A real-time Lie-group differential algebraic equations method to solve the inverse nonlinear vibration problems,” Inverse Problems in Science and Engineering, vol. 24, no. 9, pp. 1569–1586, 2016. View at Publisher · View at Google Scholar
  • Chein-Shan Liu, Wen Chen, and Li-Wei Liu, “Solving mechanical systems with nonholonomic constraints by a Lie-group differential algebraic equations method,” Journal of Engineering Mechanics, vol. 143, no. 9, 2017. View at Publisher · View at Google Scholar