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Modified Regularized Long Wave Denkleminin Nümerik Çözümü İçin Kuintik Trigonometrik B-spline Algoritması

Year 2023, Volume: 4 Issue: 2, 10 - 15, 30.06.2023

Emre Kırlı

https://doi.org/10.53608/estudambilisim.1288254
Cited By: 2

Abstract

Bu çalışma, modified regularized long-wave (MRLW) denklemini çözmek için yeni bir sayısal algoritma sunmaktadır. Konumsal değişkenleri ve türevlerini ayrıklaştırmak için kuintik trigonometrik B-spline kolokasyon tekniği kullanılır ve zamansal türev için, Adam's Moulton şeması uygulanır. Sayısal algoritmanın performans ve verimliliği, tek solitary dalganın hareketini içeren örnek problem üzerinde test edilmiştir. Hata normu ve ve üç korunum sabitleri hesaplanır ve literatürde mevcut olanlardan bazıları ile karşılaştırılır. Hesaplanan sonuçlar, önerilen algoritmanın, mevcut yöntemlere kıyasla MRLW denkleminin yüksek derecede doğru yaklaşık çözümünü elde etmede avantaja sahip olduğunu doğrulamaktadır. Yöntemin avantajı, uygulanmasının kolay olması ve düşük hesaplama maliyeti gerektirmesidir.

Keywords

Kuintik B-spline Kolokasyon Metodu Modified Regularized Long Wave Denklemi

References

  • Keskin, P., Irk, D. 2012. Numerical solution of the MRLW equation using finite difference method. International Journal of Nonlinear Science, 14(3), 355-361.
  • Ghiloufi, A., Rouatbi, A., Omrani, K. 2018. A new conservative fourth-order accurate difference scheme for solving a model of nonlinear dispersive equations. Mathematical Methods in Applied Sciences, 41(3), 1-24.
  • Bayarassou, K., Rouatbi, A., Omrani, K. 2020. Uniform error estimates of fourth-order conservative linearized difference scheme for a mathematical model for long wave. International Journal of Computer Mathematics, 97(8), 1-31.
  • Achouri, T., Omrani, K. 2010. Application of the homotopy perturbation method to the modified regularized long-wave equation. Numerical Methods for Partial Differential Equations, 26(2), 399-411.
  • Kang, X., Cheng, K., Guo, C. 2015. A secondorder Fourier pseudospectral method for the generalized regularized long wave equation. Advances in Difference Equations, 339(2015).
  • Khan, Y., Taghipour, R., Falahian, M., Nikkar, A. 2013. A new approach to modified regularized long wave equation. Neural Computing and Applications, 23(5), 1335-1341.
  • Kaplan, A. G., Dereli, Y. 2017. Numerical solutions of the MRLW equation using moving least square collocation method. Communications Series A1 Mathematics & Statistics, 66(2), 349-361.
  • Dereli, Y. 2012. Solitary wave solutions of the MRLW equation using radial basis functions. Numerical Methods for Partial Differential Equations, 28(1), 235-247.
  • Karakoc, S. B. G., Geyikli, T. 2013. PetrovGalerkin finite element method for solving the MRLW equation. Mathematical Sciences, 7(25).
  • Karakoc, S. B. G., Geyikli, T., Bashan, A. 2013. A numerical solution of the modified regularized long wave (mrlw) equation using quartic Bsplines. TWMS Journal of Applied and Engineering Mathematics, 3(2), 231-244.
  • Karakoc, S. B. G., Ucar, Y., Yagmurlu, N. 2015. Numerical solutions of the MRLW equation by cubic B-spline Galerkin finite element method. Kuwait Journal of Science, 42(2), 141-159.
  • Zorşahin, G. M., Irk, D. 2019. Numerical solution of modified regularized long wave equation by using cubic trigonometric B-spline functions. Journal of Balıkesir University Institute of Science and Technology, 21(1), 26-138.
  • Dag, I., Irk, D., Sari, M. 2013. The extended cubic B-spline algorithm for a modified regularized long wave equation, Chinese Physics B, 22(4), 040207.
  • Khalifa, A. K., Raslan, K. R., Alzubaidi, H. M. 2008. A collocation method with cubic B-splines for solving the MRLW equation. Journal of Computational and Applied Mathematics, 212(2), 406-418.
  • Raslan, K. R. 2009. Numerical study of the Modified Regularized Long Wave (MRLW) equation. Chaos Solitons and Fractals, 42(3), 1845-1853.
  • Karakoc, S. B. G., Ak, T., Zeybek, H. 2014. An efficient approach to numerical study of the MRLW equation with B-Spline collocation method. Abstract and Applied Analysis, 2014(2), 1-15.
  • Soliman, A. M. A. 2017. Collocation method using quartic B-Splines for solving the modified RLW equation. Indian Journal of Science and Technology, 10(31), 1-7.
  • Yağmurlu, N. M., Karakas, A. S. 2020. Numerical solutions of the equal width equation by trigonometric cubic B-spline collocation method based on Rubin-Graves type linearization, Numerical Methods for Partial Differential Equations, 36(5).
  • Gardner, L. R. T., Gardner, G. A., Ayoub, F. A., Amein, N. K. 1997. Approximations of solitary waves of the MRLW equation by B-spline finite element. Arabian Journal for Science and Engineering, 22(2), 183-193.

Quintic Trigonometric B-spline Algorithm for Numerical Solution of the Modified Regularized Long Wave Equation

Year 2023, Volume: 4 Issue: 2, 10 - 15, 30.06.2023

Emre Kırlı

https://doi.org/10.53608/estudambilisim.1288254
Cited By: 2

Abstract

This study introduces a new numerical algorithm for solving the modified regularized long-wave (MRLW) equation. To discretize the spatial variables and their derivatives, the collocation technique with quintic trigonometric B-spline functions is utilized and for the temporal derivative, the Adam's Moulton scheme is implemented. The performance and efficiency of the computational algorithm is tested on sample problem including the motion of single solitary wave. The error norm and three conservation constants are computed and compared with some of those available in the literature. The computed results verify that the suggested algorithm has the advantage in obtaining a highly accurate approximate solution of the MRLW equation as compared to the existing methods. The advantage of the method is that it is easy to implement and requires the low computational cost.

Keywords

Quintic Trigonometric B-spline Modified Regularized Long Wave Equation Collocation Method

References

  • Keskin, P., Irk, D. 2012. Numerical solution of the MRLW equation using finite difference method. International Journal of Nonlinear Science, 14(3), 355-361.
  • Ghiloufi, A., Rouatbi, A., Omrani, K. 2018. A new conservative fourth-order accurate difference scheme for solving a model of nonlinear dispersive equations. Mathematical Methods in Applied Sciences, 41(3), 1-24.
  • Bayarassou, K., Rouatbi, A., Omrani, K. 2020. Uniform error estimates of fourth-order conservative linearized difference scheme for a mathematical model for long wave. International Journal of Computer Mathematics, 97(8), 1-31.
  • Achouri, T., Omrani, K. 2010. Application of the homotopy perturbation method to the modified regularized long-wave equation. Numerical Methods for Partial Differential Equations, 26(2), 399-411.
  • Kang, X., Cheng, K., Guo, C. 2015. A secondorder Fourier pseudospectral method for the generalized regularized long wave equation. Advances in Difference Equations, 339(2015).
  • Khan, Y., Taghipour, R., Falahian, M., Nikkar, A. 2013. A new approach to modified regularized long wave equation. Neural Computing and Applications, 23(5), 1335-1341.
  • Kaplan, A. G., Dereli, Y. 2017. Numerical solutions of the MRLW equation using moving least square collocation method. Communications Series A1 Mathematics & Statistics, 66(2), 349-361.
  • Dereli, Y. 2012. Solitary wave solutions of the MRLW equation using radial basis functions. Numerical Methods for Partial Differential Equations, 28(1), 235-247.
  • Karakoc, S. B. G., Geyikli, T. 2013. PetrovGalerkin finite element method for solving the MRLW equation. Mathematical Sciences, 7(25).
  • Karakoc, S. B. G., Geyikli, T., Bashan, A. 2013. A numerical solution of the modified regularized long wave (mrlw) equation using quartic Bsplines. TWMS Journal of Applied and Engineering Mathematics, 3(2), 231-244.
  • Karakoc, S. B. G., Ucar, Y., Yagmurlu, N. 2015. Numerical solutions of the MRLW equation by cubic B-spline Galerkin finite element method. Kuwait Journal of Science, 42(2), 141-159.
  • Zorşahin, G. M., Irk, D. 2019. Numerical solution of modified regularized long wave equation by using cubic trigonometric B-spline functions. Journal of Balıkesir University Institute of Science and Technology, 21(1), 26-138.
  • Dag, I., Irk, D., Sari, M. 2013. The extended cubic B-spline algorithm for a modified regularized long wave equation, Chinese Physics B, 22(4), 040207.
  • Khalifa, A. K., Raslan, K. R., Alzubaidi, H. M. 2008. A collocation method with cubic B-splines for solving the MRLW equation. Journal of Computational and Applied Mathematics, 212(2), 406-418.
  • Raslan, K. R. 2009. Numerical study of the Modified Regularized Long Wave (MRLW) equation. Chaos Solitons and Fractals, 42(3), 1845-1853.
  • Karakoc, S. B. G., Ak, T., Zeybek, H. 2014. An efficient approach to numerical study of the MRLW equation with B-Spline collocation method. Abstract and Applied Analysis, 2014(2), 1-15.
  • Soliman, A. M. A. 2017. Collocation method using quartic B-Splines for solving the modified RLW equation. Indian Journal of Science and Technology, 10(31), 1-7.
  • Yağmurlu, N. M., Karakas, A. S. 2020. Numerical solutions of the equal width equation by trigonometric cubic B-spline collocation method based on Rubin-Graves type linearization, Numerical Methods for Partial Differential Equations, 36(5).
  • Gardner, L. R. T., Gardner, G. A., Ayoub, F. A., Amein, N. K. 1997. Approximations of solitary waves of the MRLW equation by B-spline finite element. Arabian Journal for Science and Engineering, 22(2), 183-193.
There are 19 citations in total.

Details

Primary Language English
Subjects Computer Software
Journal Section Research Articles
Authors

Emre Kırlı 0000-0002-5704-2370

Publication Date June 30, 2023
Submission Date April 26, 2023
Acceptance Date May 16, 2023
Published in Issue Year 2023 Volume: 4 Issue: 2

Cite

IEEE E. Kırlı, “Quintic Trigonometric B-spline Algorithm for Numerical Solution of the Modified Regularized Long Wave Equation”, ESTUDAM Bilişim, vol. 4, no. 2, pp. 10–15, 2023, doi: 10.53608/estudambilisim.1288254.

Cited By

An Improved Numerical Solution of Modified Regularized Long Wave Equation by Quartic Trigonometric B-Spline
International Journal of Applied and Computational Mathematics
https://doi.org/10.1007/s40819-025-01832-x
Adveksiyon Difüzyon Denkleminin Kuartik B-Spline En Küçük Kareler Metodu ile Sayısal Çözümü
Eskişehir Türk Dünyası Uygulama ve Araştırma Merkezi Bilişim Dergisi
https://doi.org/10.53608/estudambilisim.1310048

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