Table of Contents
Journal of Computational Engineering
Volume 2014 (2014), Article ID 346731, 12 pages
http://dx.doi.org/10.1155/2014/346731
Research Article

Wavelet Method for Numerical Solution of Parabolic Equations

Department of Mathematics, Srikishan Sarda College, Hailakandi 788151, India

Received 18 April 2013; Accepted 4 December 2013; Published 27 February 2014

Academic Editor: Fu-Yun Zhao

Copyright © 2014 A. H. Choudhury. 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. F. S. V. Bazán, “Chebyshev pseudospectral method for computing numerical solution of convection-diffusion equation,” Applied Mathematics and Computation, vol. 200, no. 2, pp. 537–546, 2008. View at Publisher · View at Google Scholar · View at Scopus
  2. B. Bradie, A Friendly Introduction to Numerical Analysis, Pearson Prentice Hall, New Delhi, India, 2006.
  3. M. Dehghan, “On the numerical solution of the one-dimensional convection-diffusion equation,” Mathematical Problems in Engineering, vol. 2005, no. 1, pp. 61–74, 2005. View at Publisher · View at Google Scholar · View at Scopus
  4. R. Glowinski, W. Lawton, M. Ravachol, and E. Tenenbaum, “Wavelet solutions of linear and nonlinear elliptic, parabolic and hyperbolic problems in one space dimension,” in Computing Methods in Applied Sciences and Engineering, R. Glowinski and A. Lichnewsky, Eds., pp. 55–120, SIAM, Philadelphia, Pa, USA, 1990. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. B. V. Rathish Kumar and M. Mehra, “A three-step wavelet Galerkin method for parabolic and hyperbolic partial differential equations,” International Journal of Computer Mathematics, vol. 83, no. 1, pp. 143–157, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. M. Mehra and B. V. Rathish Kumar, “Time-accurate solution of advection-diffusion problems by wavelet-Taylor-Galerkin method,” Communications in Numerical Methods in Engineering, vol. 21, no. 6, pp. 313–326, 2005. View at Publisher · View at Google Scholar · View at Scopus
  7. D. K. Salkuyeh, “On the finite difference approximation to the convection-diffusion equation,” Applied Mathematics and Computation, vol. 179, no. 1, pp. 79–86, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Communications on Pure and Applied Mathematics, vol. 41, no. 7, pp. 909–996, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. M. Alam, N. K.-R. Kevlahan, and O. V. Vasilyev, “Simultaneous space-time adaptive wavelet solution of nonlinear parabolic differential equations,” Journal of Computational Physics, vol. 214, no. 2, pp. 829–857, 2006. View at Publisher · View at Google Scholar · View at Scopus
  10. A. H. Choudhury and R. K. Deka, “Wavelet-Galerkin solutions of one dimensional elliptic problems,” Applied Mathematical Modelling, vol. 34, no. 7, pp. 1939–1951, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. A. H. Choudhury and R. K. Deka, “Wavelet method for numerical solution of convection-diffusion equation,” in Mathematical and Computational Models: Recent Trends, R. Nadarajan, G. A. Vijayalakshmi, Pai, and G. Sai Sundara Krishnan, Eds., Narosa Publishing House, New Delhi, India, 2010. View at Google Scholar
  12. R. K. Deka and A. H. Choudhury, “Solution of two point boundary value problems using wavelet integrals,” International Journal of Contemporary Mathematical Sciences, vol. 4, no. 13–16, pp. 695–717, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. J.-C. Xu and W.-C. Shann, “Galerkin-wavelet methods for two-point boundary value problems,” Numerische Mathematik, vol. 63, no. 1, pp. 123–144, 1992. View at Publisher · View at Google Scholar · View at Scopus
  14. A. Latto, H. L. Resnikoff, and E. Tenenbaum, “The evaluation of connection coefficients of compactly supported wavelets,” in Proceedings of the French-USA Workshop on Wavelets and Turbulence, Y. Maday, Ed., New York, NY, USA, 1994.
  15. H. L. Resnikoff and R. O. Wells, Jr., Wavelet Analysis: The Scalable Structure of Information, Springer, New York, NY, USA, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  16. J. N. Reddy, An Introduction to the Finite Element Method, Tata McGraw-Hill, New Delhi, India, 2003.