Epsilon: Jurnal Matematika Murni dan Terapan
Vol 14, No 2 (2020): JURNAL EPSILON VOLUME 14 NOMOR 2

PEMBENTUKAN PERSAMAAN VAN DER POL DAN SOLUSI MENGGUNAKAN METODE MULTIPLE SCALE

Farohatin Na'imah (Alumni Program Studi Matematika FMIPA ULM)
Yuni Yulida (Program Studi Matematika FMIPA Universitas Lambung Mangkurat)
Muhammad Ahsar Karim (Program Studi Matematika FMIPA Universitas Lambung Mangkurat)



Article Info

Publish Date
02 Mar 2021

Abstract

Mathematical modeling is one of applied mathematics that explains everyday life in mathematical equations, one example is Van der Pol equation. The Van der Pol equation is an ordinary differential equation derived from the Resistor, Inductor, and Capacitor (RLC) circuit problem. The Van der Pol equation is a nonlinear ordinary differential equations that has a perturbation term. Perturbation is a problem in the system, denoted by ε which has a small value 0<E<1. The presence of perturbation tribe result in difficulty in solving the equation using anlytical methode. One method that can solve the Van der Pol equation is a multiple  scale method. The purpose of this study is to explain the constructions process of  Van der Pol equation, analyze dynamic equations around equilibrium, and determine the solution of Van der Pol equation uses a multiple scale method. From this study it was found that the Van der Pol equation system has one equilibrium. Through stability analysis, the Van der Pol equation system will be stable if E= 0 and  -~<E<=-2. The solution of the Van der Pol equation with the multiple scale method is Keywords: Van der Pol equation, equilibrium, stability, multiple scale. 

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Journal Info

Abbrev

epsilon

Publisher

Subject

Decision Sciences, Operations Research & Management Transportation

Description

Jurnal Matematika Murni dan Terapan Epsilon is a mathematics journal which is devoted to research articles from all fields of pure and applied mathematics including 1. Mathematical Analysis 2. Applied Mathematics 3. Algebra 4. Statistics 5. Computational ...