149
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

New Rothe-wavelet method for solving telegraph equations

, &
Pages 1171-1176 | Received 21 Aug 2009, Accepted 15 Oct 2010, Published online: 10 Mar 2011

References

  • Al-Qassab , M and Nair , S . 2004 . Wavelet–Galerkin Method for the Free Vibrations of an Elastic Cable Carrying an Attached Mass . Journal of Sound and Vibration , 270 : 191 – 206 .
  • Amaratunga , K , Williams , JR , Qian , S and Weiss , J . 1994 . Wavelet–Galerkin Solution for One-dimensional Partial Differential Equations . International Journal of Numerical Methods in Engineering , 37 : 2705 – 2716 .
  • Asady , B , Kajani , MT , Vencheh , AH and Heydari , A . 2005 . Direct Method for Solving Integro Differential Equations using Hybrid Fourier and Block-pulse Functions . International Journal of Systems Science , 82 : 889 – 895 .
  • Bacry , E , Mallat , S and Papanicolau , G . 1992 . A Wavelet Based Space Time Adaptive Numerical Method for Partial Differential Equations . Mathematical Modelling and Numerical Analysis , 26 : 793 – 834 .
  • Bertoluzza , S and Verani , M . 2003 . Convergence of a Nonlinear Wavelet Algorithm for the Solution of PDEs . Applied Mathematics Letters , 16 : 113 – 118 .
  • Castro , L and Freitas , J . 2001 . Wavelet in Hybrid-mixed Stress Element . Computer Methods in Applied Mechanics and Engineering , 190 : 3977 – 3998 .
  • Christon , MA and Roach , DW . 2000 . Numerical Performance of Wavelet for PDEs: The Multi-scale Finite Element . Computational Mechanics , 25 : 230 – 244 .
  • Dahmen , W . 2001 . Wavelet Methods for PDEs – Some Recent Development . Journal of Computational and Applied Mathematics , 128 : 133 – 185 .
  • Daubechies , I . 1992 . Ten Lecture on Wavelets , Philadelphia , PA : SIAM .
  • El-Azab , MS . 2007a . A Numerical Algorithm for the Solution of Telegraph Equations . Applied Mathematics and Computation , 190 : 757 – 764 .
  • El-Azab , MS . 2007b . An Approximation Scheme for a Nonlinear Diffusion Fisher's Equation . Applied Mathematics and Computation , 186 : 579 – 588 .
  • Guo , LZ and Billings , SA . 2008 . Identification and Analysis of Spatio-temporal Dynamical Systems Using Wavelets . International Journal of Systems Science , 39 : 315 – 334 .
  • Jaffard , S and Laurencot , P . 1992 . “ Orthonormal Wavelets Analysis of Operators and Applications to Numerical Analysis ” . In Wavelets: A Tutorial in Theory and Applications , Edited by: Chui , C . 543 – 601 . New York : Academic Press .
  • Jang , G , Kim , J and Kim , Y . 2004 . Multiscale Galerkin Method using Interpolation Wavelet for Two-dimensional Elliptic Problems in General Domains . International Journal for Numerical Methods in Engineering , 59 : 225 – 253 .
  • Kačur , J . 1985 . Method of Rothe in Evolution Equations, Teubner-Texte Zur Mathematik , Vol. 80 , Leipzig : BSB B.G. Teubner Verlagsgesellschaft .
  • Ko , J , Kurdila , AJ and Pilant , MS . 1997 . Triangular Wavelet Based Finite Elements via Multivalued Scaling Equations . Computational Methods of Applied Mechanics and Engineering , 146 : 1 – 17 .
  • Lho , S and Yang , SY . 2001 . Wavelet–Galerkin Method for Solving Parabolic Equations in Finite Domains . Finite Elements in Analysis and Design , 37 : 1023 – 1037 .
  • Liatsis , P , Goulermas , JY , Zeng , XJ and Milonidis , E . 2009 . A Flexible Visual Inspection System Based on Neural Networks . International Journal of Systems Science , 40 : 173 – 186 .
  • Maleknejad , K , Kajani , MT and Mahmoudi , Y . 2003 . Numerical Solution of Linear Fredholm and Volterra Integral Equations of the Second Kind by using Legendre Wavelets . Kybernetes , 32 : 1530 – 1539 .
  • Metaxas , AC and Meredith , RJ . 1993 . Industrial Microwave Heating , London : Peter Peregrinus .
  • Mohammadi , F . Hosseini, M.M., and Mohud-Din, S.T. (2011), ‘Legendre Wavelet Galerkin Method for Solving Ordinary Differential Equations with Non Analytic Solution’, International Journal of Systems Science, 42, 579–585
  • Razzaghi , M and Yousefi , S . 2002 . Sine–Cosine Wavelets Operational Matrix of Integration and Its Applications in the Calculus of Variations . International Journal of Systems Science , 33 : 805 – 810 .
  • Roussy , G and Pearcy , JA . 1995 . Foundations and Industrial Applications of Microwaves and Radio Frequency Fields , New York : John Wiley .
  • Vudu , R . and Barkeley, U.C. (2010), ‘A Wavelet Collection Methods for Solving Partial Differential Equations’, Mathematical Report Matyh, 228B
  • Walter , GG and Shen , X . 2001 . Wavelets and Other Orthogonal Systems, , 2nd , Boca Raton , FL : Chapman and Hall/CRC .
  • Wei , HL and Billings , SA . 2004 . Identification and Reconstruction of Chaotic Systems using Multiresolution Wavelet Decompositions . International Journal of Systems Science , 35 : 511 – 526 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.