Solving Ordinary Differential Equation Using Parallel Fourth Order Runge-Kutta Method With Three Processors

Fajri, Iman Al; Mesra, Hendra; Kusuma, Jeffry; Hendra; Jeffry Kusuma

doi:10.20956/j.v17i3.12490

Open access Jurnal

Solving Ordinary Differential Equation Using Parallel Fourth Order Runge-Kutta Method With Three Processors

Penyelesaian Persamaan Diferensial Biasa Menggunakan Metode Runge-Kutta Orde Keempat Paralel dengan Tiga Prosesor

Jurnal Matematika, Statistika dan Komputasi · Vol. 17 No. 3 (2021) · pp. 349–356

DOI: 10.20956/j.v17i3.12490
ISSN: 2614-8811, 1858-1382
Published: 2021-05-12
Publisher: Department of Mathematics, Hasanuddin University
Language: en
License: creativecommons.org/licenses/by/4.0

Abstract

English

This paper presents a derivation of the Runge-Kutta or fourth method with six stages suitable for parallel implementation. Development of a parallel model based on the sparsity structure of the fourth type Runge-Kutta which is divided into three processors. The calculation of the parallel computation model and the sequential model from the accurate side shows that the sequential model is better. However, generally, the parallel method will end the analytic solution by increasing the number of iterations. In terms of execution time, parallel method has advantages over sequential method.

Bahasa Indonesia

Makalah ini menyajikan penurunan dari metode Runge-Kutta orde keempat dengan enam tahapan yang cocok untuk implementasi secara paralel. Pengembangan model paralel didasarkan pada struktur sparsity Runge-Kutta tipe kempat yang dibagi ke dalam tiga prosesor. Perbandingan perhitungan model paralel dan model sekuensial dari sisi akurasi menunjukkan bahwa model sekuensial lebih baik. Akan tetapi secara umum bahwa metode paralel akan mendekati solusi analitik dengan meningkatkan jumlah iterasi. Ditinjau dari sisi waktu eksekusi, metode paralel memiliki keunggulan dibandingkan dengan metode sekuensial.

Keywords

Collaboration network of the authors

18 authors · 28 co-authorship links · 2 across different organisations

Hover or tap a name to highlight its co-authors. Double-click to open the author's page.

Institut Teknologi Sepuluh Nopember
Hasanuddin University
Universitas Halu Oleo
Affiliation unknown

Different organisations
Same organisation
Affiliation unknown
Thicker line = more joint articles · bigger circle = more articles

Show as table

Co-author	Organisation	Joint articles
Chastine Fatichah	Institut Teknologi Sepuluh Nopember	2
Handayani Tjandrasa	Institut Teknologi Sepuluh Nopember	2
Syamsuddin Toaha	Affiliation unknown	2
ABDUL RAHMAN	Universitas Halu Oleo	1
Abdul M. Balubi	Affiliation unknown	1
Desy Lusiyanti	Affiliation unknown	1
Selvy Musdalifah	Affiliation unknown	1
Agusman Sahari	Affiliation unknown	1
Agustinus Ribal	Affiliation unknown	1
Muh Hamzah	Affiliation unknown	1
Naimah Aris	Affiliation unknown	1
Muhammad Nur Hidayat	Affiliation unknown	1
Hukmah Hukmah	Affiliation unknown	1
Ismi Ra'yan Syarif	Affiliation unknown	1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.

Original metadata (oai_dc)

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	<dc:title xml:lang="en">Solving Ordinary Differential Equation Using Parallel Fourth Order Runge-Kutta Method With Three Processors</dc:title>
	<dc:title xml:lang="id">Penyelesaian Persamaan Diferensial Biasa Menggunakan Metode Runge-Kutta Orde Keempat Paralel dengan Tiga Prosesor</dc:title>
	<dc:creator xml:lang="en">Fajri, Iman Al </dc:creator>
	<dc:creator xml:lang="en">Mesra, Hendra</dc:creator>
	<dc:creator xml:lang="en">Kusuma, Jeffry </dc:creator>
	<dc:creator xml:lang="id">Hendra</dc:creator>
	<dc:creator xml:lang="id">Jeffry Kusuma</dc:creator>
	<dc:subject xml:lang="en">Fourth Order Runge-Kutta Method</dc:subject>
	<dc:subject xml:lang="en">Parallel Algorithm</dc:subject>
	<dc:subject xml:lang="en">Sequential Algorithm</dc:subject>
	<dc:subject xml:lang="id">Metode Runge-Kutta Orde Keempat</dc:subject>
	<dc:subject xml:lang="id">Algoritma Paralel</dc:subject>
	<dc:subject xml:lang="id">Algoritma Sekuensial</dc:subject>
	<dc:description xml:lang="en">This paper presents a derivation of the Runge-Kutta or fourth method with six stages suitable for parallel implementation. Development of a parallel model based on the sparsity structure of the fourth type Runge-Kutta which is divided into three processors. The calculation of the parallel computation model and the sequential model from the accurate side shows that the sequential model is better. However, generally, the parallel method will end the analytic solution by increasing the number of iterations. In terms of execution time, parallel method has advantages over sequential method.</dc:description>
	<dc:description xml:lang="id">Makalah ini menyajikan penurunan dari metode Runge-Kutta orde keempat dengan enam tahapan yang cocok untuk implementasi secara paralel. Pengembangan model paralel didasarkan pada struktur sparsity Runge-Kutta tipe kempat yang dibagi ke dalam tiga prosesor. Perbandingan perhitungan model paralel dan model sekuensial dari sisi akurasi menunjukkan bahwa model sekuensial lebih baik. Akan tetapi secara umum bahwa metode paralel akan mendekati solusi analitik dengan meningkatkan jumlah iterasi. Ditinjau dari sisi waktu eksekusi, metode paralel memiliki keunggulan dibandingkan dengan metode sekuensial.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2021-05-12</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
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	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/12490</dc:identifier>
	<dc:identifier>10.20956/j.v17i3.12490</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 17 No. 3 (2021):  May, 2021; 349-356</dc:source>
	<dc:source>2614-8811</dc:source>
	<dc:source>1858-1382</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/12490/6705</dc:relation>
	<dc:relation>10.20956/j.v17i3.12490.g6705</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2021 Author and publisher</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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