Numerical verification of the orders of accuracy of truncated asymptotic expansion solutions to the van der Pol equation

被引：0

作者：

Sudi Mungkasi

机构：

[1] Sanata Dharma University,Department of Mathematics, Faculty of Science and Technology

来源：

Journal of Mathematical Chemistry | 2021年 / 59卷

关键词：

Asymptotic expansion; Formal expansion; Order of accuracy; Perturbation method; Van der Pol equation;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We propose a numerical method to verify the orders of accuracy of truncated asymptotic expansion solutions to the van der Pol equation. Our proposed method is simpler than an existing method (Deeba and Xie in J Comput Anal Appl 3(2): 165–171, 2001). Our proposed method does not need any technique of a least-squares fit of error data, whereas the existing one does. Numerical simulations confirm that our proposed method works effectively.

引用

页码：216 / 223

页数：7

共 50 条

[1] Numerical verification of the orders of accuracy of truncated asymptotic expansion solutions to the van der Pol equation
Mungkasi, Sudi
JOURNAL OF MATHEMATICAL CHEMISTRY, 2021, 59 (01) : 216 - 223
[2] The asymptotic expansion and numerical verification of Van der Pol's equation
Deeba, E
Xie, SS
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2001, 3 (02) : 165 - 171
[3] Analytical and numerical solutions of the Van Der Pol Equation
J. Stefan Inst, Ljubljana, Slovenia
Elektroteh Vestn Electrotech Rev, 4-5 (225-233):
[4] PERIODIC SOLUTIONS OF VAN DER POL EQUATION
ZONNEVELD, JA
KONINKLIJKE NEDERLANDSE AKADEMIE VAN WETESCHAPPEN-PROCEEDINGS SERIES A-MATHEMATICAL SCIENCES, 1966, 69 (05): : 620 - +
[5] Numerical solution to the van der Pol equation with fractional damping
Konuralp, Ali
Konuralp, Cigdem
Yildirim, Ahmet
PHYSICA SCRIPTA, 2009, T136
[6] Exact Solutions and Integrability of the Duffing - Van der Pol Equation
Kudryashov, Nikolay A.
REGULAR & CHAOTIC DYNAMICS, 2018, 23 (04): : 471 - 479
[7] Periodic solutions for van der Pol equation with time delay
Lin, Guojian
APPLIED MATHEMATICS AND COMPUTATION, 2007, 187 (02) : 1187 - 1198
[8] Exact Solutions and Integrability of the Duffing – Van der Pol Equation
Nikolay A. Kudryashov
Regular and Chaotic Dynamics, 2018, 23 : 471 - 479
[9] Computing the solutions of the van der Pol equation to arbitrary precision
Amore, Paolo
PHYSICA D-NONLINEAR PHENOMENA, 2022, 435
[10] ASYMPTOTIC WAVE SOLUTIONS FOR THE MODEL OF A MEDIUM WITH VAN DER POL OSCILLATORS
Danylenko, V. A.
Skurativskyi, S. I.
Skurativska, I. A.
UKRAINIAN JOURNAL OF PHYSICS, 2014, 59 (09): : 932 - 938

← 1 2 3 4 5 →