PEMBENTUKAN PERSAMAAN VAN DER POL DAN SOLUSI MENGGUNAKAN METODE MULTIPLE SCALE

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.