- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 768963, 13 pages
Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method
1Department of Mathematics, Science Faculty, Fırat University, 23119 Elazığ, Turkey
2Department of Mathematics, Education Faculty, Dicle University, 21280 Diyarbakır, Turkey
3Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA
4Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
Received 18 December 2012; Accepted 5 March 2013
Academic Editor: Mustafa Bayram
Copyright © 2013 Mustafa Inc 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.
- M. Dehghan, “On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation,” Numerical Methods for Partial Differential Equations, vol. 21, no. 1, pp. 24–40, 2005.
- R. K. Mohanty, M. K. Jain, and K. George, “On the use of high order difference methods for the system of one space second order nonlinear hyperbolic equations with variable coefficients,” Journal of Computational and Applied Mathematics, vol. 72, no. 2, pp. 421–431, 1996.
- E. H. Twizell, “An explicit difference method for the wave equation with extended stability range,” BIT, vol. 19, no. 3, pp. 378–383, 1979.
- R. K. Mohanty, “An unconditionally stable difference scheme for the one-space-dimensional linear hyperbolic equation,” Applied Mathematics Letters, vol. 17, no. 1, pp. 101–105, 2004.
- A. Mohebbi and M. Dehghan, “High order compact solution of the one-space-dimensional linear hyperbolic equation,” Numerical Methods for Partial Differential Equations, vol. 24, no. 5, pp. 1222–1235, 2008.
- M. Dehghan, “Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices,” Mathematics and Computers in Simulation, vol. 71, no. 1, pp. 16–30, 2006.
- M. Dehghan and A. Shokri, “A numerical method for solving the hyperbolic telegraph equation,” Numerical Methods for Partial Differential Equations, vol. 24, no. 4, pp. 1080–1093, 2008.
- H. Yao, “Reproducing kernel method for the solution of nonlinear hyperbolic telegraph equation with an integral condition,” Numerical Methods for Partial Differential Equations, vol. 27, no. 4, pp. 867–886, 2011.
- S. A. Yousefi, “Legendre multiwavelet Galerkin method for solving the hyperbolic telegraph equation,” Numerical Methods for Partial Differential Equations, vol. 26, no. 3, pp. 535–543, 2010.
- M. Dehghan and M. Lakestani, “The use of Chebyshev cardinal functions for solution of the second-order one-dimensional telegraph equation,” Numerical Methods for Partial Differential Equations, vol. 25, no. 4, pp. 931–938, 2009.
- M. Lakestani and B. N. Saray, “Numerical solution of telegraph equation using interpolating scaling functions,” Computers & Mathematics with Applications, vol. 60, no. 7, pp. 1964–1972, 2010.
- M. Dehghan and A. Ghesmati, “Solution of the second-order one-dimensional hyperbolic telegraph equation by using the dual reciprocity boundary integral equation (DRBIE) method,” Engineering Analysis with Boundary Elements, vol. 34, no. 1, pp. 51–59, 2010.
- A. N. Tikhonov and A. A. Samarskiĭ, Equations of Mathematical Physics, Dover, New York, NY, USA, 1990.
- N. Aronszajn, “Theory of reproducing kernels,” Transactions of the American Mathematical Society, vol. 68, pp. 337–404, 1950.
- M. Inc, A. Akgül, and A. Kılıçman, “Explicit solution of telegraph equation based on reproducing kernel method,” Journal of Function Spaces and Applications, vol. 2012, p. 23, 2012.
- M. Inc and A. Akgül, “The reproducing kernel Hilbert space method for solving Troesch’s problem,” Journal of the Association of Arab Universities for Basic and Applied Sciences. In press.
- M. Inc, A. Akgül, and A. Kılıçman, “A new application of the reproducing kernel Hilbert space method to solve MHD Jeffery-Hamel flows problem in nonparallel walls,” Abstract and Applied Analysis, vol. 2013, Article ID 239454, 12 pages, 2013.
- M. Inc, A. Akgül, and F. Geng, “Reproducing kernel Hilbert space method for solving Bratu’s problem,” Bulletin of the Malaysian Mathematical Sciences Society. In press.
- M. Inc, A. Akgül, and A. Kılıçman, “On solving KdV equation using reproducing kernel Hilbert space method,” Abstract and Applied Analysis, vol. 2013, Article ID 578942, 11 pages, 2013.
- W. Jiang and Y. Lin, “Representation of exact solution for the time-fractional telegraph equation in the reproducing kernel space,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 9, pp. 3639–3645, 2011.
- Y. Wang, L. Su, X. Cao, and X. Li, “Using reproducing kernel for solving a class of singularly perturbed problems,” Computers & Mathematics with Applications, vol. 61, no. 2, pp. 421–430, 2011.
- F. Geng and M. Cui, “A novel method for nonlinear two-point boundary value problems: combination of ADM and RKM,” Applied Mathematics and Computation, vol. 217, no. 9, pp. 4676–4681, 2011.
- F. Geng and F. Shen, “Solving a Volterra integral equation with weakly singular kernel in the reproducing kernel space,” Mathematical Sciences Quarterly Journal, vol. 4, no. 2, pp. 159–170, 2010.
- F. Geng and M. Cui, “Homotopy perturbation-reproducing kernel method for nonlinear systems of second order boundary value problems,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2405–2411, 2011.
- M. Cui and Y. Lin, Nonlinear Numerical Analysis in the Reproducing Kernel Space, Nova Science, New York, NY, USA, 2009.
- A. M. Krall, Hilbert Space, Boundary Value Problems and Orthogonal Polynomials, vol. 133 of Operator Theory: Advances and Applications, Birkhäuser, Basel, Switzerland, 2002.