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Stability of finite difference schemes for two-space dimensional telegraph equation

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Abstract

This paper is devoted to the study of two-dimensional hyperbolic partial differential telegraph equation. Converting the PDE to an ODE yields exact solution to this problem. Then, using first-order finite difference techniques, we obtain approximate numerical solutions. The numerical solution’s error analysis is provided. The stability estimates of finite difference schemes, as well as some numerical tests to check the correctness with regard to the precise solution are provided.

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References

  1. M E Koksal, M Senol and A Unver, Chin. J. Phys. 59, 507 (2019)

    Article  Google Scholar 

  2. A Ashyralyev and M E Koksal, Turk. J. Math. 32(4), 407 (2008)

    Google Scholar 

  3. A Ashyralyev and M E Koksal, Numer. Methods Partial Differ. Eq. 25(5), 1084 (2009)

    Google Scholar 

  4. I Fedotov, M Y Shatalov and J Marais, Acta Mech. 227(11), 3315 (2016)

    Article  MathSciNet  Google Scholar 

  5. P A Krutitskii, J. Math. Kyoto Univ. 37(2), 343 (1997)

    MathSciNet  Google Scholar 

  6. M E Koksal, Disc. Dyn. Nature Soc. 2011, 1 (2011)

    Google Scholar 

  7. M E Koksal, AIMS Math. 4(1), 61 (2019)

    Article  Google Scholar 

  8. M M Islam and M S Hasan, Afr. J. Math. Comput. Sci. Res. 11(7), 103 (2018)

    Google Scholar 

  9. A Merad and A Bouziani, J. Appl. Eng. Math. 3(2), 245 (2013)

    MathSciNet  Google Scholar 

  10. M Sari, A Gunay and G Gurarslan, Int. J. Nonlinear Sci. 17(1), 57 (2014)

    MathSciNet  Google Scholar 

  11. B Soltanalizadeh, Comput. Appl. Math. 30(3), 639 (2016)

    Article  MathSciNet  Google Scholar 

  12. M Dehghan and A Shokri, Numer. Meth. Partial Differ. Eq. 24(4), 1080 (2008)

    Article  Google Scholar 

  13. M Javidi and N Nyamoradi, Int. J. Adv. Math. Sci. 1(2), 64 (2013)

    Google Scholar 

  14. A Ashyralyev and M Modanli, Bound. Value Probl. 1, 41 (2015)

    Article  Google Scholar 

  15. M E Koksal, Disc. Dyn. Nature Soc. 2011(6), (2011)

  16. M Hosseininia and M H Heydari, Chaos Solitons Fractals 127, 389 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  17. R C Mittal and R Bhatia, Appl. Math. Comput. 244, 976 (2014)

    MathSciNet  Google Scholar 

  18. I Singh and S Kumar, J. Math. Ext. 11, 1 (2017)

    MathSciNet  Google Scholar 

  19. F Wang and E Hou, J. Math. 2020, 8832197 (2020)

    Google Scholar 

  20. M Aslefallah and D Rostamy, J. Eng. Math. 118, 1 (2019)

    Article  Google Scholar 

  21. R K Mohanty, Int. J. Comput. Math. 86, 2071 (2009)

    Google Scholar 

  22. Y Zhou and Z Luo, J. Ineq. Appl. 2018, 1 (2018)

    Article  Google Scholar 

  23. B Zogheib and E Tohidi, Comput. Math. Appl. 75, 3571 (2018)

    Article  MathSciNet  Google Scholar 

  24. A Ashyralyev and P E Sobolevskii, New difference schemes for partial differential equations (Springer Science and Business Media, 2004) Vol. 148

Download references

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Art and Science, Harran University, Sanliurfa, 63300, Turkey

    Mahmut Modanli & Fatih Ozbag

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  1. Mahmut Modanli
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  2. Fatih Ozbag
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Correspondence to Fatih Ozbag.

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Modanli, M., Ozbag, F. Stability of finite difference schemes for two-space dimensional telegraph equation. Pramana - J Phys 96, 228 (2022). https://doi.org/10.1007/s12043-022-02474-0

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  • DOI: https://doi.org/10.1007/s12043-022-02474-0

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