Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 5

Representation for the reproducing kernel Hilbert space method for a nonlinear system

Pages
1345–1355
Publication Date
2022-10-18
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)

We prove the efficiency of the method.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We apply the reproducing kernel Hilbert space method to a nonlinear system in this work.
📊
Key Findings & Data:We obtain accurate results.
💡
Conclusion & Impact:We prove the efficiency of the method.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:reproducing kernel functions · a nonlinear system · bounded linear operator

Abstract

We apply the reproducing kernel Hilbert space method to a nonlinear system in this work. We utilize this technique to overcome the nonlinearity of the problem. We obtain accurate results. We demonstrate our results by tables and figures. We prove the efficiency of the method.

🔖

Cite This Article

Akgül, E. K., Akgül, A., Khan, Y., Baleanu, D. (2022). Representation for the reproducing kernel Hilbert space method for a nonlinear system. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 5, 1345–1355. https://ajindex.com/articles/530553

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (14)

  1. S. Abbasbandy, B. Azarnavid and M. S. Alhuthali, A shooting reproducing kernel Hilbert space method for multiple solutions of nonlinear boundary value problems, J. Comput. Appl. Math., 279, 293–305, 2015
  2. A. Akgul and M. Inc, Approximate solutions for mhd squeezing fluid flow by a novel method, Boundary Value Problems, 2014, Article number: 18, 2014
  3. B. Azarnavid and K. Parand, An iterative reproducing kernel method in Hilbert space for the multi-point boundary value problems, J. Comput. Appl. Math., 328, 151–163, 2018
  4. A. H. Bhrawy, M. A. Abdelkawy, E. M. Hilal, A. A. Alshaery and A. Biswas, Solitons, cnoidal waves, snoidal waves and other solutions to Whitham-Broer-Kaup system, Appl. Math. Inf. Sci., 8 (5), 2119–2128, 2014, doi:10.12785/amis/080505
  5. A. H. Bhrawy, J. F. Alzaidy, M. A. Abdelkawy and A. Biswas, Jacobi spectral collocation approximation for multi-dimensional time-fractional Schrödinger equations, Nonlinear Dynam., 84 (3), 1553–1567, 2016, doi:10.1007/s11071-015-2588-x
  6. A. Biswas, Solitary wave solution for KdV equation with power-law nonlinearity and time-dependent coefficients, Nonlinear Dynam., 58 (1-2), 345–348, 2009, doi:10.1007/ s11071-009-9480-5
  7. D. Biswas and T. Banerjee, A simple chaotic and hyperchaotic time-delay system: design and electronic circuit implementation, Nonlinear Dynam., 83 (4), 2331–2347, 2016, doi:10.1007/s11071-015-2484-4
  8. S. Choi and J. A. Eastman, Enhancing thermal conductivity of fluids with nanoparticle, ASME FED, 231, 99–105, 1995
  9. I. Cialenco, G. E. Fasshauer and Q. Ye, Approximation of stochastic partial differential equations by a kernel-based collocation method, Int. J. Comput. Math., 89 (18), 2543– 2561, 2012
  10. M. Cui and Y. Lin, Nonlinear numerical analysis in the reproducing kernel space, Nova Science Publishers Inc., New York, 2009
  11. G. E. Fasshauer, F. J. Hickernell and Q. Ye, Solving support vector machines in reproducing kernel Banach spaces with positive definite functions, Appl. Comput. Harmon. Anal., 38 (1), 115–139, 2015
  12. F. Geng and M. Cui, Solving a nonlinear system of second order boundary value problems, J. Math. Anal. Appl., 327 (2), 1167–1181, 2007, doi:10.1016/j.jmaa.2006. 05.011
  13. M. Inc, A. Akgul and A. Kilicman, Numerical solutions of the second-order onedimensional telegraph equation based on reproducing kernel Hilbert space method, Abstr. Appl. Anal., 2013, 13 pages, 2013
  14. R. Ketabchi, R. Mokhtari and E. Babolian, Some error es