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Numerical study of integer-order hyperbolic telegraph model arising in physical and related sciences

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Abstract

More recently, it is discovered in the field of applied sciences and engineering that the telegraph equation is better suited to model reaction-diffusion than the ordinary diffusion equation. In this article, the second-order hyperbolic telegraph equations are analyzed numerically by means of an efficient local differential quadrature method utilizing the radial basis functions. The explicit time integration technique is used to semi-discretize the model in the time direction, while the space derivatives are discretized by the proposed meshless procedure. To test the accuracy and capabilities of the method, five test problems are considered utilizing both rectangular and non-rectangular domains, which show that the proposed scheme solutions are converging extremely quick in comparison with the different existing numerical techniques in the recent literature.

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Authors and Affiliations

  1. Department of Mathematics, University of Swabi, Swabi, 23430, Khyber Pakhtunkhwa, Pakistan

    Imtiaz Ahmad

  2. Department of Basic Sciences, University of Engineering and Technology Peshawar, Peshawar, Pakistan

    Hijaz Ahmad

  3. Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayyat, Saudi Arabia

    Ahmed E. Abouelregal

  4. Renewable Energy Research Centre, Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok, 1518 Pracharat 1 Road, Bangsue, Bangkok, 10800, Thailand

    Phatiphat Thounthong

  5. Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt

    M. Abdel-Aty

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  1. Imtiaz Ahmad
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  2. Hijaz Ahmad
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  3. Ahmed E. Abouelregal
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  4. Phatiphat Thounthong
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  5. M. Abdel-Aty
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Correspondence to Hijaz Ahmad.

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Ahmad, I., Ahmad, H., Abouelregal, A.E. et al. Numerical study of integer-order hyperbolic telegraph model arising in physical and related sciences. Eur. Phys. J. Plus 135, 759 (2020). https://doi.org/10.1140/epjp/s13360-020-00784-z

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  • DOI: https://doi.org/10.1140/epjp/s13360-020-00784-z

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