SavedAdd your journal

Journals / TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics / 2019 / Cilt: 9 - Sayı: 1

A NUMERICAL APPROACH TO CAUDREY DODD GIBBON EQUATION VIA COLLOCATION METHOD USING QUINTIC B-SPLINE BASIS

Berat KARAAGAC
Pages
1–8
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)

Additionally, graphical simulations of the solutions are depicted by figures.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this manuscript, a numerical approach is investigated to Caudrey-DoddGibbon (CDG) equation.
📊
Key Findings & Data:The numerical solutions together with the error norms L2, L∞ are tabulated.
💡
Conclusion & Impact:Additionally, graphical simulations of the solutions are depicted by figures.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Özet

In this manuscript, a numerical approach is investigated to Caudrey-DoddGibbon (CDG) equation. The nonlinear CDG equation is reduced to a system of partial differential equation using uxxx = v. The new numerical solutions are obtained with a combination of collocation method with finite element method which is one of the most important methods among all numerical approaches. In order to proceed the method, solution for each unknown is written as a linear combination of time parameters and quintic B-spline basis. Then, with the advantage of the collocation method, a system of algebraic equation systems is formulated easily. Solving the system iteratively by a method results in numerical solutions of the CDG equation. The numerical solutions together with the error norms L2, L∞ are tabulated. Additionally, graphical simulations of the solutions are depicted by figures.

🔖

Cite This Article

KARAAGAC, B. (2019). A NUMERICAL APPROACH TO CAUDREY DODD GIBBON EQUATION VIA COLLOCATION METHOD USING QUINTIC B-SPLINE BASIS. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, Cilt: 9 - Sayı: 1, 1–8. https://ajindex.com/articles/341264

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (13)

  1. Bulut, H., Sulaiman, T. A., Baskonus, H. M.,(2016), New solitary and optical wave structures to the Korteweg–de Vries equation with dual-power law nonlinearity, Optical and Quantum Electronics, 48.12:564, pp. 3-14
  2. Fakhar-Izadi, F., Dehghan M.,(2018), Fully spectral collocation method for nonlinear parabolic partial integro-differential equations, Applied Numerical Mathematics, 123, pp. 99-120
  3. Gnitchogna, R., Atangana, A.,(2018), New two step Laplace Adam-Bashforth method for integer a noninteger order partial differential equations, Numerical Methods for Partial Differential Equations, 34.5, pp. 1739-1758
  4. Baskonus, H. M., Sulaiman, T. A., Bulut H., (2017), On the novel wave behaviors to the coupled nonlinear Maccari’s system with complex structure, Optik-International Journal for Light and Electron Optics, 131, pp. 1036-1043
  5. Baseri, A., Abbasbandy, S., Babolian E.,(2018), A collocation method for fractional diffusion equation in a long time with Chebyshev functions, Applied Mathematics and Computation, 322, pp. 55-65
  6. Oru¸c, O., Bulut, F., Eseni A.,(2016),Numerical solutions of regularized long wave equation by haar ¨ wavelet method, Mediterranean Journal of Mathematics 13.5, pp. 3235-3253
  7. Ba¸shan, A., Yagmurlu, M. N., Ucar, Y., Esen, A., (2018), A new perspective for quintic B-spline based Crank-Nicolson-differential quadrature method algorithm for numerical solutions of the nonlinear Schr¨odinger equation, The European Physical Journal Plus, 133.1, pp. 2-15
  8. Atangana, A., Owolabi, K. M., (2018), New numerical approach for fractional differential equations, Mathematical Modelling of Natural Phenomena 13.1:3, pp. 1-21
  9. Oru¸c, O., Bulut, F., Esen A.,(2017), A numerical treatment based on Haar wavelets for coupled KdV ¨ equation, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 7.2, pp. 195-204
  10. Aiyer, R.N., Fuchssteiner, B., Oevel, W.,(1986), Solitons and discrete eigenfunctions of the recursion operator of non-linear evolution equations: the Caudrey–Dodd–Gibbon–Sawada–Kotera equations, J. Phys. A: Math. Gen. 19, pp. 3755–3770
  11. Salas, A., (2008), Some exact solutions for the Caudrey-Dodd-Gibbon equation, arXiv preprint, arXiv:0805.2969
  12. Abdollahzadeh, M. et al., (2010), Exact travelling solutions for fifth order Caudrey-Dodd-Gibbon equation, International Journal of Applied Mathematics and Computation, 2.4, 81-90
  13. Naher, H., Abdullah, F. A., Akbar, M. A.,(201