A Rothe-Chebyshev collocation algorithm for the hyperbolic telegraphic type equations with variable coefficients
We construct a semi-discretized spectral approach for the second-order telegraphic-type equations with Dirichlet or Neumann boundary conditions. The successive method of Rothe is first employed for the temporal discretization procedure to transform the model equations into a system of boundary value...
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| Published in: | Ain Shams Engineering Journal Vol. 16; no. 11; p. 103720 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.11.2025
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| ISSN: | 2090-4479 |
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| Abstract | We construct a semi-discretized spectral approach for the second-order telegraphic-type equations with Dirichlet or Neumann boundary conditions. The successive method of Rothe is first employed for the temporal discretization procedure to transform the model equations into a system of boundary value problems. Subsequently, the spectral matrix procedure utilizing the shifted modified Chebyshev polynomials (SMCPs) is formulated for the spatial variable. The family of discrete solutions obtained by the hybrid Rothe-SMCPs algorithm is demonstrated to exhibit uniform convergence to the continuous solution of order O(Δτ+R−3). In this context, Δτ signifies the time step, while R represents the number of SMCPs employed in the approximation procedure. Simulation experiments are carried out to highlight the strong agreement between the numerical results and theoretical predictions. The numerical results utilizing a larger time-step size exhibit greater accuracy compared to the computational values available in existing research works. |
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| AbstractList | We construct a semi-discretized spectral approach for the second-order telegraphic-type equations with Dirichlet or Neumann boundary conditions. The successive method of Rothe is first employed for the temporal discretization procedure to transform the model equations into a system of boundary value problems. Subsequently, the spectral matrix procedure utilizing the shifted modified Chebyshev polynomials (SMCPs) is formulated for the spatial variable. The family of discrete solutions obtained by the hybrid Rothe-SMCPs algorithm is demonstrated to exhibit uniform convergence to the continuous solution of order O(Δτ+R−3). In this context, Δτ signifies the time step, while R represents the number of SMCPs employed in the approximation procedure. Simulation experiments are carried out to highlight the strong agreement between the numerical results and theoretical predictions. The numerical results utilizing a larger time-step size exhibit greater accuracy compared to the computational values available in existing research works. |
| ArticleNumber | 103720 |
| Author | Ahmed, H.M. Noeiaghdam, Samad Izadi, Mohammad |
| Author_xml | – sequence: 1 givenname: Mohammad orcidid: 0000-0002-6116-4928 surname: Izadi fullname: Izadi, Mohammad email: izadi@uk.ac.ir organization: Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran – sequence: 2 givenname: Samad orcidid: 0000-0002-2307-0891 surname: Noeiaghdam fullname: Noeiaghdam, Samad email: snoei@hnas.ac.cn organization: Institute of Mathematics, Henan Academy of Sciences, Zhengzhou 450046, China – sequence: 3 givenname: H.M. orcidid: 0000-0002-5643-8357 surname: Ahmed fullname: Ahmed, H.M. email: hanyahmed@techedu.helwan.edu.eg organization: Department of Mathematics, Faculty of Technology and Education, Helwan University, Cairo 11281, Egypt |
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| Cites_doi | 10.1007/s12190-024-02273-3 10.1186/s13661-024-01944-1 10.1007/s13540-023-00184-x 10.1016/j.cpc.2014.10.013 10.1016/j.camwa.2019.03.011 10.1002/num.22957 10.1016/j.chaos.2025.116569 10.3390/sym13122370 10.1007/s10092-023-00557-x 10.1007/s40819-023-01656-7 10.1002/num.20442 10.1080/00150517.2002.12428647 10.1016/S0377-0427(02)00861-0 10.1016/j.aml.2011.04.026 10.1016/j.jocs.2024.102450 10.1142/S0219876218501189 10.1186/s13662-020-03085-y 10.5614/j.math.fund.sci.2020.52.3.6 10.1093/qjmam/4.2.129 10.1140/epjp/i2017-11529-2 10.1007/BF01782368 10.3934/math.2023558 10.3390/math11010032 10.1007/s40096-021-00428-y 10.1142/S0218348X22401661 10.1504/IJCSM.2022.128185 10.1155/2014/526814 10.1016/j.jmaa.2005.12.020 10.1007/s40096-020-00357-2 10.1016/j.camwa.2017.08.020 10.1088/0266-5611/9/6/013 10.1007/s00009-019-1375-1 10.1080/00207721.2010.547626 10.1186/s13661-025-02085-9 10.1007/s40819-020-00903-5 10.1063/1.369258 |
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| Issue | 11 |
| Keywords | Collocation nodes 65N12 35B25 Error estimation 65M70 41A10 Hyperbolic telegraphic equation Time-horizontal Rothe's approach Modified Chebyshev polynomials Convergence analysis |
| Language | English |
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| SubjectTerms | Collocation nodes Convergence analysis Error estimation Hyperbolic telegraphic equation Modified Chebyshev polynomials Time-horizontal Rothe's approach |
| Title | A Rothe-Chebyshev collocation algorithm for the hyperbolic telegraphic type equations with variable coefficients |
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