Bernstein polynomials for solving nonlinear stiff system of ordinary differential equations

Mohammed Alshbool; Ishak Hashim

doi:10.1063/1.4931342

Bernstein polynomials for solving nonlinear stiff system of ordinary differential equations

Mohammed Alshbool
, Ishak Hashim

Universiti Kebangsaan Malaysia

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

In this paper, Bernstein polynomials method (B-polynomials) is applied to solve nonlinear stiff systems of ordinary differential equations. We present an approximate solution that depends on Bernstein polynomials method and collocation points. The procedure of the method will be explained briefly and illustrative examples are included to demonstrate the validity of the method. The results of B-polynomials are compared with other several methods that solved nonlinear stiff system of ordinary differential equations. The results revealed the accuracy of the proposed method.

Original language	English
Title of host publication	2015 UKM FST Postgraduate Colloquium
Subtitle of host publication	Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2015 Postgraduate Colloquium
Editors	Mohd Shahrul Mohd Nadzir, Humaida Banu Samsudin, Marlia Mohd Hanafiah, Asmat Ahmad, Nurul Izzaty Hassan, Izfa Riza Hazmi, Hani Kartini Agustar, Zahari Ibarahim, Noor Baa'yah Ibrahim, Sakhinah Abu Bakar, Mohd Salmi Md Noorani, Nurul Huda Abd Karim, Saiful Irwan Zubairi, Nazlina Ibrahim
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735413252
DOIs	https://doi.org/10.1063/1.4931342
State	Published - 25 Sep 2015
Externally published	Yes
Event	2015 Postgraduate Colloquium of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology, UKM FST 2015 - Selangor, Malaysia Duration: 15 Apr 2015 → 16 Apr 2015

Publication series

Name	AIP Conference Proceedings
Volume	1678
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	2015 Postgraduate Colloquium of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology, UKM FST 2015
Country/Territory	Malaysia
City	Selangor
Period	15/04/15 → 16/04/15

Keywords

Bernstein Polynomials
Stiff System

Access to Document

10.1063/1.4931342

Cite this

Alshbool, M., & Hashim, I. (2015). Bernstein polynomials for solving nonlinear stiff system of ordinary differential equations. In M. S. M. Nadzir, H. B. Samsudin, M. M. Hanafiah, A. Ahmad, N. I. Hassan, I. R. Hazmi, H. K. Agustar, Z. Ibarahim, N. B. Ibrahim, S. Abu Bakar, M. S. M. Noorani, N. H. A. Karim, S. I. Zubairi, & N. Ibrahim (Eds.), 2015 UKM FST Postgraduate Colloquium: Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2015 Postgraduate Colloquium Article 060015 (AIP Conference Proceedings; Vol. 1678). American Institute of Physics Inc.. https://doi.org/10.1063/1.4931342

Alshbool, Mohammed ; Hashim, Ishak. / Bernstein polynomials for solving nonlinear stiff system of ordinary differential equations. 2015 UKM FST Postgraduate Colloquium: Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2015 Postgraduate Colloquium. editor / Mohd Shahrul Mohd Nadzir ; Humaida Banu Samsudin ; Marlia Mohd Hanafiah ; Asmat Ahmad ; Nurul Izzaty Hassan ; Izfa Riza Hazmi ; Hani Kartini Agustar ; Zahari Ibarahim ; Noor Baa'yah Ibrahim ; Sakhinah Abu Bakar ; Mohd Salmi Md Noorani ; Nurul Huda Abd Karim ; Saiful Irwan Zubairi ; Nazlina Ibrahim. American Institute of Physics Inc., 2015. (AIP Conference Proceedings).

@inproceedings{368d126d42044633a22f4c987d7c5df6,

title = "Bernstein polynomials for solving nonlinear stiff system of ordinary differential equations",

abstract = "In this paper, Bernstein polynomials method (B-polynomials) is applied to solve nonlinear stiff systems of ordinary differential equations. We present an approximate solution that depends on Bernstein polynomials method and collocation points. The procedure of the method will be explained briefly and illustrative examples are included to demonstrate the validity of the method. The results of B-polynomials are compared with other several methods that solved nonlinear stiff system of ordinary differential equations. The results revealed the accuracy of the proposed method.",

keywords = "Bernstein Polynomials, Stiff System",

author = "Mohammed Alshbool and Ishak Hashim",

note = "Publisher Copyright: {\textcopyright} 2015 AIP Publishing LLC.; 2015 Postgraduate Colloquium of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology, UKM FST 2015 ; Conference date: 15-04-2015 Through 16-04-2015",

year = "2015",

month = sep,

day = "25",

doi = "10.1063/1.4931342",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Nadzir, \{Mohd Shahrul Mohd\} and Samsudin, \{Humaida Banu\} and Hanafiah, \{Marlia Mohd\} and Asmat Ahmad and Hassan, \{Nurul Izzaty\} and Hazmi, \{Izfa Riza\} and Agustar, \{Hani Kartini\} and Zahari Ibarahim and Ibrahim, \{Noor Baa'yah\} and \{Abu Bakar\}, Sakhinah and Noorani, \{Mohd Salmi Md\} and Karim, \{Nurul Huda Abd\} and Zubairi, \{Saiful Irwan\} and Nazlina Ibrahim",

booktitle = "2015 UKM FST Postgraduate Colloquium",

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Alshbool, M & Hashim, I 2015, Bernstein polynomials for solving nonlinear stiff system of ordinary differential equations. in MSM Nadzir, HB Samsudin, MM Hanafiah, A Ahmad, NI Hassan, IR Hazmi, HK Agustar, Z Ibarahim, NB Ibrahim, S Abu Bakar, MSM Noorani, NHA Karim, SI Zubairi & N Ibrahim (eds), 2015 UKM FST Postgraduate Colloquium: Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2015 Postgraduate Colloquium., 060015, AIP Conference Proceedings, vol. 1678, American Institute of Physics Inc., 2015 Postgraduate Colloquium of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology, UKM FST 2015, Selangor, Malaysia, 15/04/15. https://doi.org/10.1063/1.4931342

Bernstein polynomials for solving nonlinear stiff system of ordinary differential equations. / Alshbool, Mohammed; Hashim, Ishak.
2015 UKM FST Postgraduate Colloquium: Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2015 Postgraduate Colloquium. ed. / Mohd Shahrul Mohd Nadzir; Humaida Banu Samsudin; Marlia Mohd Hanafiah; Asmat Ahmad; Nurul Izzaty Hassan; Izfa Riza Hazmi; Hani Kartini Agustar; Zahari Ibarahim; Noor Baa'yah Ibrahim; Sakhinah Abu Bakar; Mohd Salmi Md Noorani; Nurul Huda Abd Karim; Saiful Irwan Zubairi; Nazlina Ibrahim. American Institute of Physics Inc., 2015. 060015 (AIP Conference Proceedings; Vol. 1678).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Bernstein polynomials for solving nonlinear stiff system of ordinary differential equations

AU - Alshbool, Mohammed

AU - Hashim, Ishak

PY - 2015/9/25

Y1 - 2015/9/25

N2 - In this paper, Bernstein polynomials method (B-polynomials) is applied to solve nonlinear stiff systems of ordinary differential equations. We present an approximate solution that depends on Bernstein polynomials method and collocation points. The procedure of the method will be explained briefly and illustrative examples are included to demonstrate the validity of the method. The results of B-polynomials are compared with other several methods that solved nonlinear stiff system of ordinary differential equations. The results revealed the accuracy of the proposed method.

AB - In this paper, Bernstein polynomials method (B-polynomials) is applied to solve nonlinear stiff systems of ordinary differential equations. We present an approximate solution that depends on Bernstein polynomials method and collocation points. The procedure of the method will be explained briefly and illustrative examples are included to demonstrate the validity of the method. The results of B-polynomials are compared with other several methods that solved nonlinear stiff system of ordinary differential equations. The results revealed the accuracy of the proposed method.

KW - Bernstein Polynomials

KW - Stiff System

UR - https://www.scopus.com/pages/publications/85006207122

U2 - 10.1063/1.4931342

DO - 10.1063/1.4931342

M3 - Conference contribution

AN - SCOPUS:85006207122

T3 - AIP Conference Proceedings

BT - 2015 UKM FST Postgraduate Colloquium

A2 - Nadzir, Mohd Shahrul Mohd

A2 - Samsudin, Humaida Banu

A2 - Hanafiah, Marlia Mohd

A2 - Ahmad, Asmat

A2 - Hassan, Nurul Izzaty

A2 - Hazmi, Izfa Riza

A2 - Agustar, Hani Kartini

A2 - Ibarahim, Zahari

A2 - Ibrahim, Noor Baa'yah

A2 - Abu Bakar, Sakhinah

A2 - Noorani, Mohd Salmi Md

A2 - Karim, Nurul Huda Abd

A2 - Zubairi, Saiful Irwan

A2 - Ibrahim, Nazlina

PB - American Institute of Physics Inc.

T2 - 2015 Postgraduate Colloquium of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology, UKM FST 2015

Y2 - 15 April 2015 through 16 April 2015

ER -

Alshbool M, Hashim I. Bernstein polynomials for solving nonlinear stiff system of ordinary differential equations. In Nadzir MSM, Samsudin HB, Hanafiah MM, Ahmad A, Hassan NI, Hazmi IR, Agustar HK, Ibarahim Z, Ibrahim NB, Abu Bakar S, Noorani MSM, Karim NHA, Zubairi SI, Ibrahim N, editors, 2015 UKM FST Postgraduate Colloquium: Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2015 Postgraduate Colloquium. American Institute of Physics Inc. 2015. 060015. (AIP Conference Proceedings). doi: 10.1063/1.4931342

Bernstein polynomials for solving nonlinear stiff system of ordinary differential equations

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