KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 6

Fractal quintic spline method for nonlinear boundary-value problems

S. Natesan
N. Balasubramani
M. Guru Prem Prasad
Sayfa
1885–1903
Yayın Tarihi
2022-10-18
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)

Numerical examples are provided to show practical usefulness of the method and numerical results are compared with the existing numerical methods.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this article, numerical solutions of nonlinear boundary-value problems are obtained using fractal quintic spline.
📊
Temel Bulgular & Veri:Convergence analysis of the proposed method is also established.
💡
Sonuç & Katkı:Numerical examples are provided to show practical usefulness of the method and numerical results are compared with the existing numerical methods.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:fractal quintic spline · nonlinear boundary-value problem · quasilinearization

Abstract

In this article, numerical solutions of nonlinear boundary-value problems are obtained using fractal quintic spline. Convergence analysis of the proposed method is also established. Proposed method has fourth-order convergence. Numerical examples are provided to show practical usefulness of the method and numerical results are compared with the existing numerical methods.

🔖

Bu Makaleye Atıf Yap

Natesan, S., Balasubramani, N., Prasad, M. G. P. (2022). Fractal quintic spline method for nonlinear boundary-value problems. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 6, 1885–1903. https://ajindex.com/articles/529557

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (17)

  1. M. Baccouch, A superconvergent local discontinuous Galerkin method for nonlinear two-point boundary-value problems, Numer. Algor. 79 (3), 697–718, 2018
  2. M. Baccouch, An adaptive local discontinuous Galerkin method for nonlinear twopoint boundary-value problems, Numer. Algor. 2019, doi:10.1007/s11075-019-00794-8
  3. M.F. Barnsley, Fractal functions and interpolation, Constr. Approx. 2 (1), 303–329, 1986
  4. M.F. Barnsley and A.N. Harrington, The calculus of fractal interpolation functions, J. Approx. Theory 57 (1), 14–34, 1989
  5. R.E. Bellman and R.E. Kalaba, Quasilinearization and Nonlinear Boundary-Value Problems, American Elsevier, New York, 1965
  6. R. Bhatia, L. Elsner, and G. Krause, Bounds for the variation of the roots of a polynomial and the eigenvalues of a matrix, Linear Algebra Appl. 142, 195–209, 1990
  7. S.K. Bhatta and K.S. Sastri, A sixth order spline procedure for a class of nonlinear boundary-value problems, Int. J. Comput. Math. 49 (3–4), 255–271, 1993
  8. S.K. Bhatta and K.S. Sastri, Symmetric spline procedures for boundary-value problems with mixed boundary conditions, J. Comput. Appl. Math. 45 (3), 237–250, 1993
  9. A.K.B. Chand and G.P. Kapoor, Generalized cubic spline fractal interpolation functions, SIAM J. Numer. Anal. 44 (2), 655–676, 2006
  10. A.K.B. Chand and P. Viswanathan, A constructive approach to cubic hermite fractal interpolation function and its constrained aspects, BIT 53 (4), 841–865, 2013
  11. M.M. Chawla, A sixth order tridiagonal finite difference method for nonlinear twopoint boundary-value problems, BIT 17 (2), 128–133, 1977
  12. M.M. Chawla, An eighth order tridiagonal finite difference method for nonlinear twopoint boundary-value problems, BIT 17 (3), 281–285, 1977
  13. M.M. Chawla and P.N. Shivakumar, Numerov’s method for nonlinear two-point boundary-value problems, Int. J. Comput. Math. 17 (2), 167–176, 1985
  14. M.M. Chawla and R. Subramanian, A new fourth-order cubic spline method for nonlinear two-point boundary-value problems, Int. J. Comput. Math. 22 (3-4), 321–341, 1987
  15. M.M. Chawla and R. Subramanian, A new fourth-order cubic spline method for second-order nonlinear two-point boundary-value problems, J. Comput. Appl. Math. 23 (1), 1–10, 1988
  16. M.M. Chawla, R. Subramanian, and P.N. Shivakumar, Numerov’s method for nonlinear two-point boundary-value problems II. monotone approximations, Int. J. Comput. Math. 26 (3-4), 219–227, 1989
  17. U. Erdogan and T. Ozis, A smart nonsta