SOLUSI PERSAMAAN EMDEN-FOWLER ORDE DUA DENGAN MEMANFAATKAN MATRIKS OPERASIONAL DARI POLINOMIAL BERNSTEIN

  • Yudhi Yudhi Universitas Tanjungpura
  • Evi Noviani Universitas Tanjungpura
  • Sarah Aljona
Keywords: Emden-Fowler equations, operational Bernstein Polynomial matrix, integral operational, differential operational

Abstract

Dalam penelitian ini, matriks operasional dari Polinomial Bernstein digunakan untuk mengaproksimasi solusi Persamaan Emden-Fowler orde dua. Untuk mencari solusi Persamaan Emden-Fowler digunakan matriks operasional integral dan matriks operasional diferensial dari Polinomial Bernstein. Karena Persamaan Emden-Fowler berorde dua, maka  digunakan dalam matriks operasional dari Polinomial Bernstein.  Berdasarkan hasil penelitian bahwa solusi Persamaan Emden Fowler dengan  diperoleh galat yang lebih kecil daripada dengan , baik menggunakan matriks operasional integral maupun matriks operasional diferensial dari Polinomial Bernstein

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References

S.C. Sihombing dan A. Dahlia, “Penyelesaian Persamaan Diferensial Linear Orde Satu dan Dua disertai Nilai Awal dengan menggunakan Metode Runge Kutta Orde Lima Butcher dan Felhberg (RKF45), Jurnal matematika Integratif, vol. 14, no. 1, Mei 2018.

F., Fardinah, “Solusi Persamaan Diferensial Biasa dengan Metode Runge-Kutta Orde Limaâ€, Journal MSA, vol. 5, no. 1, Jan-Juni 2017.

R., Munir, Metode Numerik, Bandung : Informatika, 2003.

A. M., Wazwaz, “Adomian Decomposition Method for a Reliable Treatment of the Emden-Fowler Equationâ€, Applied Mathematics and Computation, vol. 161, 543-560, 2005

S. A. Yousefi dan M. Behroozifar , “Operational matrices of polinomial bernsteins and their applicationsâ€, Journal of Systems Science, vol. 46, pp. 709-716, Maret 2010.

A. Isah dan C. Phang, “A collocation Method based on Genocchi operational matrix for solving Emden Fowler Equationsâ€, Journal of Physics, vol. :1-9, 2020

R. Singh, V. Guleria, dan M. Singh, “Haar wavelet Quasilinearization Method for Numerical Solution of Emden Fowler type Equationsâ€, Mathematics and Coomputers in Simulation, vol. 174, 123-13, 2020

R.K.M. Pandey dan N. Kumar, “Solution of lane-emden type equations using bernstein operational matrix of differentiationâ€, New Astronomy, vol. 17, pp. 303-308, September 2011.

M. Panjaitan, “Pemahaman Metode Numerik Menggunakan Pemograman Matlabâ€, JurTI, vol. 1, no.1 : 89-94, Juli 2017

A. Saadatmandi, “Bernstein operational matrix of fractional derivatives and its applicationsâ€, Applied Mathematical Modelling, vol. 38, no. : 1365-1372, August 2013

I. L. Freire, P. L. da Silva dan M. Torrisi, “Lie and noether symmetries for a class of fouth-order Emden-Fowler equationsâ€, Journal of Physics A: Mathematical and Theoretical, vol. 46, no. 24, Juni 2013.

G.E. Chatzarakis, S.R. Grace, I. Jadlovska dll., “Oscillation criteria for third-order Emden-Fowler differential equations with unbounded neutral coefficientsâ€, Hindawi Complexity, vol. 2019, Agustus 2019.

B. Ibis, â€Approximate analytical solutions for nonlinear Emden-Fowler type equations by differential transform methodâ€, arXiv preprint arXiv: 1211.3521, 2012.

A. Kalamajska dan K. Mazowiecka, “Some regularity results to the generalized Emden-Fowler equation with irreguler dataâ€, Math.Methods Appl.Sci., vol. 38, no. 12, hal. 2479-2495, Juni 2015.

P. Guha, “Generalized Emden-Fowler equation in noncentral curl forces and first integralsâ€, Acta Mechanica, vol. 231, no. 2, hal. 815-825, Februari 2020.

A.S. Bataineh, O. R. Isik, A.K. Alomari dll, “An efficient scheme for time-dependent Emden-Fowler type equations based on two-dimensional Bernstein polynomialsâ€, Mathematics, vol. 8,no. 9, 1473, September 2020.

Published
2021-06-01
How to Cite
[1]
Y. Yudhi, E. Noviani, and S. Aljona, “SOLUSI PERSAMAAN EMDEN-FOWLER ORDE DUA DENGAN MEMANFAATKAN MATRIKS OPERASIONAL DARI POLINOMIAL BERNSTEIN”, BAREKENG: J. Math. & App., vol. 15, no. 2, pp. 335-346, Jun. 2021.