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Abstract and Applied Analysis
Volume 2015, Article ID 712584, 9 pages
Research Article

Power Series Solution for Solving Nonlinear Burgers-Type Equations

1Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil
2Departamento de Ciências Exatas e Tecnológicas, Universidade Estadual de Santa Cruz, Campus Soane Nazaré de Andrade, Rodovia Jorge Amado, Km 16, Bairro Salobrinho, 45662-900 Ilhéus, BA, Brazil
3Departamento de Física, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Apartado Postal 14-740, 07000 México, DF, Mexico

Received 20 October 2014; Revised 9 March 2015; Accepted 10 March 2015

Academic Editor: Fazal M. Mahomed

Copyright © 2015 E. López-Sandoval 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. G. Zill, A First Course in Differential Equations—The Classic, Brooks/Cole, 5th edition, 2001.
  2. L. Yilmaz, “Some considerations on the series solution of differential equations and its engineering applications,” RMZ Materials and Geo-Environment, vol. 53, no. 1, pp. 247–259, 2006. View at Google Scholar
  3. C. Lin, C.-W. Wang, and X.-L. Zhang, “Series solution for the Schrodinger equation with a long-range spherically symmetric potential,” Proceedings of the Royal Society of London A, vol. 458, no. 2022, pp. 1285–1290, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. C. Lin and M.-M. Lin, “Series solution of the differential equation determining the nth-shell one-electron density of a bare Coulomb problem in quantum physics,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, pp. 677–681, 2008. View at Publisher · View at Google Scholar
  5. E. H. Doha, D. Baleanu, A. H. Bhrawy, and M. A. Abdelkawy, “A jacobi collocation method for solving nonlinear burgers-type equations,” Abstract and Applied Analysis, vol. 2013, Article ID 760542, 12 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  6. J. P. Boyd, Chebyshev and Fourier Spectral Methods, Dover, 2nd edition, 2001,
  7. J. P. Boyd and F. Yu, “Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan-Sheppridge polynomials, Chebyshev-Fourier Series, cylindrical Robert functions, Bessel-Fourier expansions, square-to-disk conformal mapping and radial basis functions,” Journal of Computational Physics, vol. 230, no. 4, pp. 1408–1438, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. C. H. Kim and U. J. Choi, “Spectral collocation methods for a partial integro-differential equation with a weakly singular kernel,” Australian Mathematical Society Journal Series B: Applied Mathematics, vol. 39, no. 3, pp. 408–430, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  9. M. Javidi and A. Golbabai, “Spectral collocation method for parabolic partial differential equations with Neumann boundary conditions,” Applied Mathematical Sciences, vol. 1, no. 5-8, pp. 211–218, 2007. View at Google Scholar · View at MathSciNet
  10. A. H. Khater, R. S. Temsah, and M. M. Hassan, “A Chebyshev spectral collocation method for solving Burgers'-type equations,” Journal of Computational and Applied Mathematics, vol. 222, no. 2, pp. 333–350, 2008. View at Publisher · View at Google Scholar
  11. E. López-Sandoval, A. Mello, and J. J. Godina-Nava, “Power series solution to non-linear partial differential equations of mathematical physics,”
  12. C. P. Filipich, L. T. Villa, and R. O. Grossi, “The power series method in the effectiveness factor calculations,” Latin American Applied Research, vol. 40, no. 3, pp. 207–212, 2010. View at Google Scholar
  13. C. P. Filipich, M. B. Rosales, and F. Buezas, “Some nonlinear mechanical problems solved with analytical solutions,” Latin American Applied Research, vol. 34, no. 2, pp. 101–109, 2004. View at Google Scholar · View at Scopus
  14. P. P. Banerjee, “A simplified approach to solving nonlinear dispersive equations using a power series method,” Proceedings of the IEEE, vol. 74, no. 9, pp. 1288–1290, 1986. View at Publisher · View at Google Scholar
  15. V. Fairen, V. Lopez, and L. Conde, “Power series approximation to solutions of nonlinear systems of differential equations,” American Journal of Physics, vol. 56, pp. 57–61, 1988. View at Google Scholar
  16. A. S. Nuseir and A. Al-Hasson, “Power series solution for nonlinear system of partial differential equations,” Applied Mathematical Sciences, vol. 6, no. 104, pp. 5147–5159, 2012. View at Google Scholar
  17. H. Quevedo, “General static axisymmetric solution of Einstein's vacuum field equations in prolate spheroidal coordinates,” Physical Review D: Particles and Fields, vol. 39, no. 10, pp. 2904–2911, 1989. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. J. Hadamard, “Sur les problèmes aux dérivées partielles et leur signification physique,” Princeton University Bulletin, vol. 13, pp. 49–52, 1902. View at Google Scholar