# Second Order Non linear ode matlab

1. Oct 2, 2015

### SteliosVas

1. The problem statement, all variables and given/known data

Okay the problem is of a free swinging pendulum with dampening which is modelled using the following equation:

Damping coefficient: c=1 s−1
Mass: m=1 kg
Gravity: g=9.81 ms−1

We know
θ(0)=90° and θ′(0)=0, solve this equation from t = 0 to t = 10 with a time interval of 0.01s

The equation is:

d2θ/dt2+(c/m)*(dθ/dt)+(g/l)*sin (θ)=0

So we need to use Euler,Heun and 4th order Runge-Kutta method

2. Relevant equations

3. The attempt at a solution

Okay so my idea was to create a function as so:

function xdot=pendemo(t,x)

% PENDEMO Pendulum ODE derivative evaluation

xdot(1,1) = x(2,1);

xdot(2,1) = -1/(1*1)*x(2,1) - 9.81/1*sin(x(1,1));

% End of pendemo.m

and than an m.file giving the above information:

xphi = [pi/2;0];

tphi = 0; 5 %start time

tfin = 10; %end time

[t,x] = ode45('pendemo',[tphi tfin],xphi);

plot(t,x(:,1))

The only thing is how do I implement a euler/heun method? What is a 4th order Runga Kata??

thanks

2. Oct 6, 2015

### BvU

Did you try to google something ? I found several matlab RK4 integrator codes in no time at all !

3. Oct 6, 2015