Consider the van der Pol equation: (d 2 x/dt 2 )- µ(1 x 2 ) dx/dt + x A sin(t) =
ID: 3421724 • Letter: C
Question
Consider the van der Pol equation:
(d2x/dt2)- µ(1 x2 ) dx/dt + x A sin(t) = 0, (1)
where f(t) = A sin(t) is a driving function; µ 0 is a scalar parameter indicating the nonlinearity and the strength of damping.
For more information about the van der Pol equation, check out its wikipedia webpage. Convert this problem into a system of 2 first order ODEs and develop a matlab program to solve the van der Pol equation using the Runge-Kutta-Fehlberg method.
Your program can not use any of the the matlab built-in functions for solving ODEs. You should turn in a .m file RKFxxx.m which contains a matlab function of the form function [Tout,Xout,DXout,info] = RKFxxx(T0,Tfinal,X0,DX0,tol,A,Mu,omega) where xxx is your student id; T0,Tfinal are the initial and final time, respectively; X0, DX0 are the values of x and x 0 at time T0, respectively. Your program will be tested in several cases:
1. (30 points) µ = 0 and A = 0; and
2. (30 points) µ > 0 and A = 0; and
3. (40 points) µ > 0 and A 6= 0.
Your program will receive 0 points if any of the matlab ode functions are used in your .m file.
Explanation / Answer
Consider the van der Pol equation: (d 2 x/dt 2 )- µ(1 x 2 ) dx/dt + x A sin(t) =