Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 982810, 7 pages
http://dx.doi.org/10.1155/2013/982810
Research Article
Wavelet-Based Homotopy Analysis Method for Nonlinear Matrix System and Its Application in Burgers Equation
Hebei University of Engineering, Handan 056038, China
Received 17 March 2013; Accepted 14 June 2013
Academic Editor: Evangelos J. Sapountzakis
Copyright © 2013 Xing Ruyi. 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
- S. J. Liao, On the proposed homotopy analysis technique for nonlinear problems and its applications [Ph.D. dissertation], Shanghai Jiao Tong University, 1992.
- S. J. Liao, “An approximate solution technique not depending on small parameters: a special example,” International Journal of Non-Linear Mechanics, vol. 30, no. 3, pp. 371–380, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- S. J. Liao, “A kind of approximate solution technique which does not depend upon small parameters—II. An application in fluid mechanics,” International Journal of Non-Linear Mechanics, vol. 32, no. 5, pp. 815–822, 1997. View at Google Scholar · View at Scopus
- S. J. Liao, “Homotopy analysis method: a kind of nonlinear analytical technique not depending on small parameters,” Shanghai J. Mech, vol. 18, no. 3, pp. 196–200, 1997. View at Google Scholar
- S. J. Liao, Beyond Perturbation: Introduction to the HomoTopy Analysis Method, Champan and Hall/CRC Press, Boca Raton, Fla, USA, 2003.
- M. Sajid and T. Hayat, “The application of homotopy analysis method to thin film flows of a third order fluid,” Chaos, Solitons & Fractals, vol. 38, no. 2, pp. 506–515, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- M. Sajid, T. Hayat, and S. Asghar, “Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt,” Nonlinear Dynamics, vol. 50, no. 1-2, pp. 27–35, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- S. J. Liao, “On the homotopy analysis method for nonlinear problems,” Applied Mathematics and Computation, vol. 147, no. 2, pp. 499–513, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- S. Abbasbandy, Y. Tan, and S. J. Liao, “Newton-homotopy analysis method for nonlinear equations,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1794–1800, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- T. Hayat, M. Khan, and M. Ayub, “On the explicit analytic solutions of an Oldroyd 6-constant fluid,” International Journal of Engineering Science, vol. 42, no. 2, pp. 123–135, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- S. Abbasbandy, “The application of homotopy analysis method to nonlinear equations arising in heat transfer,” Physics Letters A, vol. 360, no. 1, pp. 109–113, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- A. H. Nayfeh, Perturbation Methods, John Wiley & sons, New York, NY, USA, 2000.
- J. A. Murdock, Perturbation Methods, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, UK, 1991.
- J.-H. He, “Asymptotic methods for solitary solutions and compactons,” Abstract and Applied Analysis, vol. 2012, Article ID 916793, 130 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J.-H. He, “Addendum: new interpretation of homotopy perturbation method,” International Journal of Modern Physics B, vol. 20, no. 18, pp. 2561–2568, 2006. View at Publisher · View at Google Scholar · View at Scopus
- S.-L. Mei, “Construction of target controllable image segmentation model based on homotopy perturbation technology,” Abstract and Applied Analysis, vol. 2013, Article ID 131207, 8 pages, 2013. View at Publisher · View at Google Scholar
- W. X. Zhong, “On precise integration method,” Journal of Computational and Applied Mathematics, vol. 163, no. 1, pp. 59–78, 2004. View at Publisher · View at Google Scholar · View at Scopus
- W. X. Zhong, “Precise time-integration method for structural dynamics,” Journal of Dalian University of Technology, vol. 34, no. 2, pp. 131–136, 1994. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- W. X. Zhong, “Combined method for the solution of asymmetric Riccati differential equations,” Computer Methods in Applied Mechanics and Engineering, vol. 191, no. 1-2, pp. 93–102, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- S. Bertoluzza and G. Naldi, “A wavelet collocation method for the numerical solution of partial differential equations,” Applied and Computational Harmonic Analysis, vol. 3, no. 1, pp. 1–9, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- S.-L. Mei, Q.-S. Lu, and S.-W. Zhang, “Adaptive wavelet precise integration method for partial differential equations,” Chinese Journal of Computational Physics, vol. 21, no. 6, pp. 523–530, 2004. View at Google Scholar · View at Scopus
- S.-L. Mei, Q.-S. Lu, S.-W. Zhang, and L. Jin, “Adaptive interval wavelet precise integration method for partial differential equations,” Applied Mathematics and Mechanics, vol. 26, no. 3, pp. 364–371, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- S.-L. Mei, H.-L. Lv, and Q. Ma, “Construction of interval wavelet based on restricted variational principle and its application for solving differential equations,” Mathematical Problems in Engineering, vol. 2008, Article ID 629253, 14 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- D.-C. Wan and G.-W. Wei, “The study of quasi wavelets based numerical method applied to burgers' equations,” Applied Mathematics and Mechanics, vol. 21, no. 10, pp. 1099–1110, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- G. W. Wei, “Quasi wavelets and quasi interpolating wavelets,” Chemical Physics Letters, vol. 296, no. 3-4, pp. 253–258, 1998. View at Google Scholar · View at Scopus