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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 542839, 9 pages
http://dx.doi.org/10.1155/2013/542839
Research Article

New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds

1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
2Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt

Received 7 August 2013; Revised 13 September 2013; Accepted 13 September 2013

Academic Editor: Soheil Salahshour

Copyright © 2013 W. M. Abd-Elhameed 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.

Citations to this Article [16 citations]

The following is the list of published articles that have cited the current article.

  • W. M. Abd-Elhameed, E. H. Doha, and Y. H. Youssri, “New Spectral Second Kind Chebyshev Wavelets Algorithm for Solving Linear and Nonlinear Second-Order Differential Equations Involving Singular and Bratu Type Equations,” Abstract and Applied Analysis, 2013. View at Publisher · View at Google Scholar
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  • Xiuling Yin, and Yanqin Liu, “Symplectic Schemes for Linear Stochastic Schrödinger Equations with Variable Coefficients,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014. View at Publisher · View at Google Scholar
  • W. M. Abd-Elhameed, and Y. H. Youssri, “New Ultraspherical Wavelets Spectral Solutions for Fractional Riccati Differential Equations,” Abstract and Applied Analysis, vol. 2014, pp. 1–8, 2014. View at Publisher · View at Google Scholar
  • A. H. Bhrawy, “A New Legendre Collocation Method for Solving a Two-Dimensional Fractional Diffusion Equation,” Abstract and Applied Analysis, vol. 2014, pp. 1–10, 2014. View at Publisher · View at Google Scholar
  • R. Rajaraman, and G. Hariharan, “An efficient wavelet based spectral method to singular boundary value problems,” Journal of Mathematical Chemistry, 2015. View at Publisher · View at Google Scholar
  • E.H. Doha, W.M. Abd-Elhameed, and Y.H. Youssri, “New ultraspherical wavelets collocation method for solving 2nth-order initial and boundary value problems,” Journal of the Egyptian Mathematical Society, 2015. View at Publisher · View at Google Scholar
  • Seyed Hossein Mahdavi, and Hashim Abdul Razak, “An Efficient Iterative Scheme Using Family of Chebyshev’s Operations,” Mathematical Problems in Engineering, vol. 2015, pp. 1–10, 2015. View at Publisher · View at Google Scholar
  • W. M. Abd-Elhameed, “Some Algorithms for Solving Third-Order Boundary Value Problems Using Novel Operational Matrices of Generalized Jacobi Polynomials,” Abstract and Applied Analysis, vol. 2015, pp. 1–10, 2015. View at Publisher · View at Google Scholar
  • P. K. Sahu, and S. Saha Ray, “Chebyshev wavelet method for numerical solutions of integro-differential form of Lane–Emden type differential equations,” International Journal of Wavelets, Multiresolution and Information Processing, pp. 1750015, 2016. View at Publisher · View at Google Scholar
  • G. Hariharan, R. Rajaraman, and D. Sathiyaseelan, “Wavelet based spectral algorithm for nonlinear dynamical systems arising in ship dynamics,” Ocean Engineering, vol. 126, pp. 321–328, 2016. View at Publisher · View at Google Scholar
  • S.C. Shiralashetti, and S. Kumbinarasaiah, “Theoretical study on continuous polynomial wavelet bases through wavelet series collocation method for nonlinear Lane–Emden type equations,” Applied Mathematics and Computation, vol. 315, pp. 591–602, 2017. View at Publisher · View at Google Scholar
  • M Khaleghi, E Babolian, and S Abbasbandy, “Chebyshev reproducing kernel method: application to two-point boundary value problems,” Advances in Difference Equations, vol. 2017, no. 1, 2017. View at Publisher · View at Google Scholar
  • Fengying Zhou, and Xiaoyong Xu, “Numerical Solution of Time-Fractional Diffusion-Wave Equations via Chebyshev Wavelets Collocation Method,” Advances in Mathematical Physics, vol. 2017, pp. 1–17, 2017. View at Publisher · View at Google Scholar