PENYELESAIAN PERSAMAAN RICCATI DENGAN MENGGUNAKAN METODE DEKOMPOSISI ADOMIAN LAPLACE

Authors

  • Wartono Wartono Fakultas Sains dan Teknologi Universitas Islam Negeri (UIN) Sultan Syarif Kasim Riau

DOI:

https://doi.org/10.24014/sitekin.v11i1.562

Keywords:

Metode Dekomposisi Adomian Laplace, Persamaan Diferensial Biasa Nonlinear, Persamaan Riccati

Abstract

Makalah ini membahas tentang penyelesaian persamaan diferensial Riccati  dengan menggunakan metode dekomposisi Adomian Laplace (LADM). Metode dekomposisi Adomian Laplace merupakan metode semi analitik untuk menyelesaikan persamaan diferensial nonlinier yang mengkombinasikan antara tranformasi Laplace dan metode dekomposisi Adomian. Berdasarkan hasil perhitungan, metode dekomposisi Adomian Laplace dapat menghampiri penyelesaian persamaan diferensial biasa nonlinear.

Author Biography

Wartono Wartono, Fakultas Sains dan Teknologi Universitas Islam Negeri (UIN) Sultan Syarif Kasim Riau


     

References

Abbasbandy, S. “Homotopy pertuba-tion method for quadratic Riccati differential equation and comparison with Adomian’s decomposition method”. Applied Mathematics and Computation, 172, pp. 485 490. 2006.

Bahnasawi, A. A. El-Tawil, M. A and Abdel-Naby, A. “Solving Riccati differential equation using Adomian decomposition method. Applied Mathematics and Computation. 157. pp. 503 514. 2004.

Batiha, B., Noorani, M.S.M., and Hashim, I. “Application of Variational Iteration Method to a General Riccati Equation”. International Mathematical Forum. 2(56). pp. 2759 2770. 2007.

Biazar, J & Eslami, M. “Differential Transform Method for Quadratic Riccati Differential Equation”. International Journal of Nonlinear Science, 9(4), pp. 444 447. 2010

Kiymaz, O. “An Algorithm for Solving Initial value Problems Using Laplace Adomian Decomposition Method ”. Applied Mathematical Sciences. 3(30). pp. 1453 1459. 2009.

Polyanin, A. D. “Handbook of exact solution for ordinary differenatial equations. CRC, Florida. 2003.

Jafari, H & Tajadodi, H. He’s variational iteration methods for solving fractional Riccati differential equation. International Journal of Differential Equations. Pp. 1 – 8. 2010.

Reid, W. T. “Riccati differenatial equations (Mathematics sciences and engineering). Academis press, New York. 1972.

Syam, M. I and Hamdan, A. “An efficient method for solving Bratu equations”, Applied Mathematics and Computation. 176. pp. 704 713. 2006.

Yusufoglu, E. “Numerical solution of Duffing equation by the Laplace decomposition algorithm”, Applied Mathematics and Computation. 177. pp. 572 580. 2006.

Downloads

Published

2014-11-04

Issue

Vol. 11 No. 1 (2013): Desember 2013

Section

Articles

License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License

 

Copyright Notice

An author who publishes in the SITEKIN Journal agrees to the following terms:

  • Author retains the copyright and grants the journal the right of first publication of the work simultaneously licensed under the Creative Commons Attribution-ShareAlike 4.0 License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal
  • Author is able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book) with the acknowledgement of its initial publication in this journal.
  • Author is  permitted and encouraged to post his/her  work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of the published work (See The Effect of Open Access).

Read more about the Creative Commons Attribution-ShareAlike 4.0 Licence here: https://creativecommons.org/licenses/by-sa/4.0/.