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Block Backward Differentiation Formula Method for Solving Van der Pol Equation

Jurnal Matematika, Statistika dan Komputasi · Vol. 21 No. 3 (2025) · pp. 855–867

DOI
10.20956/j.v21i3.43390
ISSN
2614-8811, 1858-1382
Published
2025-05-14
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

The Van der Pol equation is often used as a basic model for oscillatory systems in physics and biology, such as the interaction of two plates on geological faults as well as oscillations in various electrical and electronic systems. The Van der Pol equation is a second-order nonlinear differential equation known to have stiffness properties, especially for large values of the μ parameter. This study aims to develop the Block Backward Differentiation Formula method that is applied in a block manner to solve the Van der Pol equation that is reduced to a system of first-order differential equations. This method is proven to be effective for solving Van der Pol equation with various values of μ parameter, although it requires a fairly small step size to achieve convergence at larger values of μ parameter. The resulting solutions are close to the results provided by Matlab solvers, namely ODE45 and ODE15s

Keywords

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Kurnia Novita SariAffiliation unknown1
Sapto Wahyu IndratnoAffiliation unknown1
Andi FitriawatiAffiliation unknown1

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">Block Backward Differentiation Formula Method for Solving Van der Pol Equation</dc:title>
	<dc:creator xml:lang="en">Febrianti, Werry</dc:creator>
	<dc:creator xml:lang="en">Saputra, Jova Edri</dc:creator>
	<dc:subject xml:lang="en">Numerical Method</dc:subject>
	<dc:subject xml:lang="en">BBDF</dc:subject>
	<dc:subject xml:lang="en">Van der Pol</dc:subject>
	<dc:subject xml:lang="en">Stiffness</dc:subject>
	<dc:description xml:lang="en">The Van der Pol equation is often used as a basic model for oscillatory systems in physics and biology, such as the interaction of two plates on geological faults as well as oscillations in various electrical and electronic systems. The Van der Pol equation is a second-order nonlinear differential equation known to have stiffness properties, especially for large values of the μ parameter. This study aims to develop the Block Backward Differentiation Formula method that is applied in a block manner to solve the Van der Pol equation that is reduced to a system of first-order differential equations. This method is proven to be effective for solving Van der Pol equation with various values of μ parameter, although it requires a fairly small step size to achieve convergence at larger values of μ parameter. The resulting solutions are close to the results provided by Matlab solvers, namely ODE45 and ODE15s</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2025-05-14</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/43390</dc:identifier>
	<dc:identifier>10.20956/j.v21i3.43390</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 21 No. 3 (2025): MAY 2025; 855-867</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/43390/12812</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2025 Jurnal Matematika, Statistika dan Komputasi</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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