Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 49 Sayı: 6, 1885 - 1903, 08.12.2020
https://doi.org/10.15672/hujms.452998

Öz

Kaynakça

  • [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 nonstandard finite difference scheme for second order nonlinear boundary-value problems, J. Comput. Phys. 230 (17), 6464–6474, 2011.
  • [18] P. Henrici, Discrete variable methods in ordinary differential equations, John Wiley and Sons, New York, 1962.
  • [19] M.K. Kadalbajoo and K.C. Patidar, Spline techniques for solving singularly-perturbed nonlinear problems on nonuniform grids, J. Optim. Theory Appl. 114 (3), 573–591, 2002.
  • [20] M. Lees, Discrete method for nonlinear two-point boundary-value problems, in: Numerical Solution of Partial Differential Equations, ed. J.H. Bramble, Academic Press, New York, 1966.
  • [21] L.B. Liu, H.W. Liu, and Y. Chen, Polynomial spline approach for solving second-order boundary-value problems with Neumann conditions, Appl. Math. Comput. 217 (16), 6872–6882, 2011.
  • [22] J. Rashidinia, R. Mohammadi, and R. Jalilian, Spline solution of nonlinear singular boundary-value problems, Int. J. Comput. Math. 85 (1), 39–52, 2008.
  • [23] A.S.V. Ravikanth and V. Bhattacharya, Cubic spline for a class of nonlinear singular boundary-value problems arising in physiology, Appl. Math. Comput. 174 (1), 768– 774, 2006.
  • [24] S.B.G. Karakoç, N.M. Yagmurlu, and Y. Ucar, Numerical approximation to a solution of the modified regularized long wave equation using quintic B-splines, Bound. Value Probl. 2013 (1), 2013.
  • [25] I.A. Tirmizi and E.H. Twizell, Higher-order finite-difference methods for nonlinear second-order two-point boundary-value problems, Appl. Math. Lett. 15 (7), 897–902, 2002.
  • [26] H. Zeybek and S.B.G. Karakoç, Application of the collocation method with B-splines to the GEW equation, Electron. Trans. Numer. Anal. 46, 71–88, 2017.

Fractal quintic spline method for nonlinear boundary-value problems

Yıl 2020, Cilt: 49 Sayı: 6, 1885 - 1903, 08.12.2020
https://doi.org/10.15672/hujms.452998

Öz

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.

Kaynakça

  • [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 nonstandard finite difference scheme for second order nonlinear boundary-value problems, J. Comput. Phys. 230 (17), 6464–6474, 2011.
  • [18] P. Henrici, Discrete variable methods in ordinary differential equations, John Wiley and Sons, New York, 1962.
  • [19] M.K. Kadalbajoo and K.C. Patidar, Spline techniques for solving singularly-perturbed nonlinear problems on nonuniform grids, J. Optim. Theory Appl. 114 (3), 573–591, 2002.
  • [20] M. Lees, Discrete method for nonlinear two-point boundary-value problems, in: Numerical Solution of Partial Differential Equations, ed. J.H. Bramble, Academic Press, New York, 1966.
  • [21] L.B. Liu, H.W. Liu, and Y. Chen, Polynomial spline approach for solving second-order boundary-value problems with Neumann conditions, Appl. Math. Comput. 217 (16), 6872–6882, 2011.
  • [22] J. Rashidinia, R. Mohammadi, and R. Jalilian, Spline solution of nonlinear singular boundary-value problems, Int. J. Comput. Math. 85 (1), 39–52, 2008.
  • [23] A.S.V. Ravikanth and V. Bhattacharya, Cubic spline for a class of nonlinear singular boundary-value problems arising in physiology, Appl. Math. Comput. 174 (1), 768– 774, 2006.
  • [24] S.B.G. Karakoç, N.M. Yagmurlu, and Y. Ucar, Numerical approximation to a solution of the modified regularized long wave equation using quintic B-splines, Bound. Value Probl. 2013 (1), 2013.
  • [25] I.A. Tirmizi and E.H. Twizell, Higher-order finite-difference methods for nonlinear second-order two-point boundary-value problems, Appl. Math. Lett. 15 (7), 897–902, 2002.
  • [26] H. Zeybek and S.B.G. Karakoç, Application of the collocation method with B-splines to the GEW equation, Electron. Trans. Numer. Anal. 46, 71–88, 2017.
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

N Balasubramani 0000-0001-8281-8997

M. Guru Prem Prasad Bu kişi benim 0000-0002-4484-231X

S Natesan Bu kişi benim 0000-0001-7527-1989

Yayımlanma Tarihi 8 Aralık 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 49 Sayı: 6

Kaynak Göster

APA Balasubramani, N., Guru Prem Prasad, M., & Natesan, S. (2020). Fractal quintic spline method for nonlinear boundary-value problems. Hacettepe Journal of Mathematics and Statistics, 49(6), 1885-1903. https://doi.org/10.15672/hujms.452998
AMA Balasubramani N, Guru Prem Prasad M, Natesan S. Fractal quintic spline method for nonlinear boundary-value problems. Hacettepe Journal of Mathematics and Statistics. Aralık 2020;49(6):1885-1903. doi:10.15672/hujms.452998
Chicago Balasubramani, N, M. Guru Prem Prasad, ve S Natesan. “Fractal Quintic Spline Method for Nonlinear Boundary-Value Problems”. Hacettepe Journal of Mathematics and Statistics 49, sy. 6 (Aralık 2020): 1885-1903. https://doi.org/10.15672/hujms.452998.
EndNote Balasubramani N, Guru Prem Prasad M, Natesan S (01 Aralık 2020) Fractal quintic spline method for nonlinear boundary-value problems. Hacettepe Journal of Mathematics and Statistics 49 6 1885–1903.
IEEE N. Balasubramani, M. Guru Prem Prasad, ve S. Natesan, “Fractal quintic spline method for nonlinear boundary-value problems”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 6, ss. 1885–1903, 2020, doi: 10.15672/hujms.452998.
ISNAD Balasubramani, N vd. “Fractal Quintic Spline Method for Nonlinear Boundary-Value Problems”. Hacettepe Journal of Mathematics and Statistics 49/6 (Aralık 2020), 1885-1903. https://doi.org/10.15672/hujms.452998.
JAMA Balasubramani N, Guru Prem Prasad M, Natesan S. Fractal quintic spline method for nonlinear boundary-value problems. Hacettepe Journal of Mathematics and Statistics. 2020;49:1885–1903.
MLA Balasubramani, N vd. “Fractal Quintic Spline Method for Nonlinear Boundary-Value Problems”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 6, 2020, ss. 1885-03, doi:10.15672/hujms.452998.
Vancouver Balasubramani N, Guru Prem Prasad M, Natesan S. Fractal quintic spline method for nonlinear boundary-value problems. Hacettepe Journal of Mathematics and Statistics. 2020;49(6):1885-903.