Table of Contents Author Guidelines Submit a Manuscript
International Journal of Differential Equations
Volume 2015, Article ID 762034, 8 pages
http://dx.doi.org/10.1155/2015/762034
Research Article

Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations

Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 41335-1914, Rasht 4193822697, Iran

Received 6 July 2015; Accepted 19 October 2015

Academic Editor: Patricia J. Y. Wong

Copyright © 2015 Jafar Biazar and Mohammad Hosami. 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. E. J. Kansa, “Multiquadrics—a scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates,” Computers & Mathematics with Applications, vol. 19, no. 8-9, pp. 127–145, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. E. J. Kansa, “Multiquadrics—a scattered data approximation scheme with applications to computational fluid-dynamics. II. Solutions to parabolic, hyperbolic and elliptic partial differential equations,” Computers & Mathematics with Applications, vol. 19, no. 8-9, pp. 147–161, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. S. R. Idelsohn and E. Oñate, “To mesh or not to mesh. That is the question...,” Computer Methods in Applied Mechanics and Engineering, vol. 195, no. 37–40, pp. 4681–4696, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. M. Bozzini, L. Lenarduzzi, and R. Schaback, “Adaptive interpolation by scaled multiquadrics,” Advances in Computational Mathematics, vol. 16, no. 4, pp. 375–387, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. R. Schaback and H. Wendland, “Adaptive greedy techniques for approximate solution of large RBF systems,” Numerical Algorithms, vol. 24, no. 3, pp. 239–254, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. Y. C. Hon, R. Schaback, and X. Zhou, “An adaptive greedy algorithm for solving large RBF collocation problems,” Numerical Algorithms, vol. 32, no. 1, pp. 13–25, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. Y. C. Hon, “Multiquadric collocation method with adaptive technique for problems with boundary layer,” International Journal of Applied Science and Computations, vol. 6, no. 3, pp. 173–184, 1999. View at Google Scholar · View at MathSciNet
  8. J. Behrens and A. Iske, “Grid-free adaptive semi-Lagrangian advection using radial basis functions,” Computers & Mathematics with Applications, vol. 43, no. 3–5, pp. 319–327, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. V. Pereyra and E. G. Sewell, “Mesh selection for discrete solution of boundary problems in ordinary differential equations,” Numerische Mathematik, vol. 23, no. 3, pp. 261–268, 1974. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. J. Kautsky and N. K. Nichols, “Equidistributing meshes with constraints,” SIAM Journal on Scientific and Statistical Computing, vol. 1, no. 4, pp. 499–511, 1980. View at Publisher · View at Google Scholar · View at MathSciNet
  11. T. Belytschko, Y. Krongauz, D. Organ, M. Fleming, and P. Krysl, “Meshless methods: an overview and recent developments,” Computer Methods in Applied Mechanics and Engineering, vol. 139, no. 1–4, pp. 3–47, 1996. View at Publisher · View at Google Scholar · View at Scopus
  12. W. E. Schiesser, The Numerical Method of Lines: Integration of Partial Differential Equations, Academic Press, San Diego, Calif, USA, 1991. View at MathSciNet
  13. S. A. Sarra, “Adaptive radial basis function methods for time dependent partial differential equations,” Applied Numerical Mathematics, vol. 54, no. 1, pp. 79–94, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. T. A. Driscoll and A. R. Heryudono, “Adaptive residual subsampling methods for radial basis function interpolation and collocation problems,” Computers & Mathematics with Applications, vol. 53, no. 6, pp. 927–939, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. G. E. Fasshauer, Meshfree Approximation Methods with MATLAB, World Scientific, Singapore, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  16. E. J. Kansa and R. E. Carlson, “Improved accuracy of multiquadric interpolation using variable shape parameters,” Computers & Mathematics with Applications, vol. 24, no. 12, pp. 99–120, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. S. Rippa, “An algorithm for selecting a good value for the parameter c in radial basis function interpolation,” Advances in Computational Mathematics, vol. 11, no. 2-3, pp. 193–210, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. W. Cao, W. Huang, and R. D. Russell, “A study of monitor functions for two dimensional adaptive mesh generation,” SIAM Journal on Scientific Computing, vol. 20, no. 6, pp. 1978–1994, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. G. F. Carey and H. T. Dinh, “Grading functions and mesh redistribution,” SIAM Journal on Numerical Analysis, vol. 22, no. 5, pp. 1028–1040, 1985. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus