KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2023 / Cilt: 52 - Sayı: 2

Numerical solutions of Troesch and Duffing equations by Taylor wavelets

Gökçe ÖZALTUN
Sevin GÜMGÜM
Sayfa
292–302
Yayın Tarihi
2023-03-31
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Results show that the proposed method yields highly accurate solutions by using quite low degree polynomials.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:The aim of this study is to obtain accurate numerical results for the Troesch and Duffing equations by using Taylor wavelets.
📊
Temel Bulgular & Veri:The effectiveness and accuracy of the applied method is illustrated by solving these problems for several variables.
💡
Sonuç & Katkı:Results show that the proposed method yields highly accurate solutions by using quite low degree polynomials.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Taylor wavelets · Troesch equation · Duffing equation

Abstract

The aim of this study is to obtain accurate numerical results for the Troesch and Duffing equations by using Taylor wavelets. Important features of the method include easy implementation and simple calculation. The effectiveness and accuracy of the applied method is illustrated by solving these problems for several variables. One of the important variable is the resolution parameter which enables to use low degree polynomials and decrease the computational cost. Results show that the proposed method yields highly accurate solutions by using quite low degree polynomials.

🔖

Bu Makaleye Atıf Yap

ÖZALTUN, G., GÜMGÜM, S. (2023). Numerical solutions of Troesch and Duffing equations by Taylor wavelets. Hacettepe Journal of Mathematics and Statistics, Cilt: 52 - Sayı: 2, 292–302. https://ajindex.com/articles/886280

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (16)

  1. M.A. Al-Jawary and S.G. Abd-Al-Razaq, Analytic and numerical solution for Duffing equations, Int. J. Basic Appl. Sci. 5 (2), 115-119, 2016
  2. N. Alias, A. Manaf, A. Ali and M. Habib, Solving Troesch’s problem by using modified nonlinear shooting method, J. Teknol. 78 (4-4), 45-52, 2011
  3. A. Anapalı, Ö. Yalçın and M. Gülsu, Numerical solutions of Duffing equations involving linear integral with shifted Chebyshev polynomials, AKU-J. Sci. Eng. 15, 1-11, 2015
  4. G.B. Arfken and H.J. Weber, Mathematical Methods for Physicists, Elsevier, London, 2005
  5. A. Beléndez, D.I. Méndez, E. Fernández, S. Marini and I. Pascual, An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method, Phys. Lett. A. 373 (32), 2805-2809, 2009
  6. M. Ben-Romdhane and H. Temimi, A novel computational method for solving Troesch’s problem with high-sensitivity parameter, Int. J. Comput. Meth. Eng. Sci. Mech. 18 (4-5), 230-237, 2017
  7. M. Bisheh-Niasar, A. Saadatmandi and M. Akrami-Arani, A new family of high-order difference schemes for the solution of second order boundary value problems, IJMC 9 (3), 187-199, 2018
  8. B. Bülbül and M. Sezer, Numerical solution of Duffing equation by using an improved Taylor matrix method, J. Appl Math. 2013, (6pp), 2013
  9. S.H. Chang, A variational iteration method for solving Troesch’s problem, J. Comput. Appl. Math. 234 (10), 3043-3047, 2010
  10. S.H. Chang and I.L. Chang, A new algorithm for calculating one-dimensional differential transform of nonlinear functions, Appl. Math. Comput. 195 (2), 799-808, 2008
  11. E. Deeba, S.A. Khuri and S. Xiei, An algorithm for solving boundary value problems, J. Comput. Phys. 159 (2), 125-138, 2000
  12. E.H. Doha, D. Baleanu, A.H. Bhrawi and R.M. Hafez, A Jacobi collocation method for Troesch’s problem in plasma physics, P. Romanian Acad. A 15 (2), 130-138, 2014
  13. M. El-Gamel, Numerical solution of Troesch’s problem by Sinc-collocation method Appl. Math. 4 (4), 707-712, 2013
  14. M. El-Gamel and M. Sameeh, A Chebyshev collocation method for solving Troesch’s problem, IJMCAR 3 (2), 23-32, 2013
  15. X. Feng, L. Mei and G. He, An efficient algorithm for solving Troesch’s problem, Appl. Math. Comput. 189 (1), 500507, 2007
  16. U. Filobello-Nino, H. Vazquez-Leal, B. Benhammouda, A. Perez-Sesma and J. Cervantes-Perez, Perturbation method and Laplace-Pade approximation as a novel tool to find approximate solutions for Troesch’s problem, Nova Scientia 7 (14), 57-73,