SavedAdd your journal

Journals / Adıyaman Üniversitesi Fen Bilimleri Dergisi / 2019 / Cilt: 9 - Sayı: 2

Numerical Approximation of the Combined KdV-mKdV Equation via the Quintic B-Spline Differential Quadrature Method

Kombine KdV-mKdV Denkleminin Kuintik B-Splayn Diferansiyel Kuadratür Yöntemiyle Sayısal Yaklaşımlar

Yusuf UÇAR
N. Murat YAĞMURLU
Ali BAŞHAN
Pages
386–403
Publication Date
2022-10-12
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The newly found numerical approximations have been compared to available numerical approximations and this comparison has shown that the proposed method is an efficient one for solving

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, quintic B-spline differential quadrature method (QBDQM) has been used to obtain the numerical approximation of the combined Korteweg-de Vries and modified Korteweg-de Vries equation (combined KdV-mKdV).
📊
Key Findings & Data:The efficiency and effectiveness of the proposed method has been tested by computing the maximum error norm L_infinity and discrete root mean square error L_2.
💡
Conclusion & Impact:The newly found numerical approximations have been compared to available numerical approximations and this comparison has shown that the proposed method is an efficient one for solving
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, quintic B-spline differential quadrature method (QBDQM) has been used to obtain the numerical approximation of the combined Korteweg-de Vries and modified Korteweg-de Vries equation (combined KdV-mKdV). The efficiency and effectiveness of the proposed method has been tested by computing the maximum error norm L_infinity and discrete root mean square error L_2. The newly found numerical approximations have been compared to available numerical approximations and this comparison has shown that the proposed method is an efficient one for solving

Özet

Bu makalede, kombine Korteweg-de Vries ve modifiye edilmiş Korteweg-de Vries denkleminin (kombine KdV-mKdV) sayısal yaklaşımını elde etmek için kuintik B-spline diferansiyel kuadratür yöntemi (QBDQM) uygulanmıştır. Yöntemin etkinliği ve doğruluğu, maksimum hata normu L_infinity ve ayrık kök ortalama kare hatası L_2 hesaplanarak ölçülmüştür. Yeni elde edilen sayısal sonuçlar, yayınlanan sayısal sonuçlarla karşılaştırıldı ve karşılaştırma, yöntemin, kombine KdV-mKdV denklemini çözmek için etkili bir sayısal şema olduğunu göstermiştir. Aynı zamanda bir kararlılık analizi de yapılmıştır.

🔖

Cite This Article

UÇAR, Y., YAĞMURLU, N. M., BAŞHAN, A. (2022). Numerical Approximation of the Combined KdV-mKdV Equation via the Quintic B-Spline Differential Quadrature Method. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 9 - Sayı: 2, 386–403. https://ajindex.com/articles/428472

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. Wadati, M., Wave propagation in nonlinear lattice I, Journal of the Physical Soceity of Japan, 38(3), 673-680, 1975
  2. Wadati, M., Wave propagation in nonlinear lattice II, Journal of the Physical Soceity of Japan, 38(3), 681-686, 1975
  3. Taha, T.R., Inverse scattering transform numerical schemes for nonlinear evolution equations and the method of lines, Applied Numerical Mathematics, 20, 181-187, 1996
  4. Fan, E., Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics, Chaos Soliton Fract, 16, 819–39, 2003
  5. Peng, Y., New exact solutions to the combined KdV and mKdV equation, International Journal Theoretical Physics, 42(4), 863–868, 2003
  6. Bekir, A., On traveling wave solutions to combined KdV–mKdV equation and modified Burgers–KdV equation, Communications in Nonlinear Science and Numerical Simulation, 14, 1038–1042, 2009
  7. Lu, D., Shi, Q., New solitary wave solutions for the combined KdV-MKdV equation, Journal of Information & Computational Science, 7, 1733-1737, 2010
  8. Bellman, R., Kashef, B. G., Casti, J., Differential quadrature: a tecnique for the rapid solution of nonlinear differential equations, Journal of Computational Physics, Vol. 10, 40-52, 1972
  9. Shu, C., Differential Quadrature and Its Application in Engineering, Springer-Veralg London Ltd., London, 2000
  10. Bellman, R., Kashef, B., Lee, E.S., Vasudevan, R., Differential quadrature and splines, Computers and Mathematics with Applications, Pergamon, Oxford, 1(3-4), 371-376, 1975
  11. Quan, J.R., Chang, C.T., New sightings in involving distributed system equations by the quadrature methods-I, Computers and Chemical Engineering, 13, 779-88, 1989
  12. Quan, J.R., Chang, C.T., New sightings in involving distributed system equations by the quadrature methods-II, Computers and Chemical Engineering, 13, 1017-1024, 1989
  13. Shu, C., Richards, B.E., Application of generalized differential quadrature to solve two dimensional incompressible Navier-Stokes equations, International Journal for Numerical Methods in Fluids, 15, 791-798, 1992
  14. Shu, C., Xue, H., Explicit computation of weighting coefficients in the harmonic differential quadrature, Journal of Sound and Vibration, 204(3), 549-55, 1997
  15. Zhong, H., Spline-based differential quadrature for fourth order equations and its application to Kirchhoff plates, Applied Mathematical Modelling, 28, 353-66, 2004
  16. Guo, Q. and Zhong, H., Non-linear vibration analys