How to solve 2nd order DE with Explicit Euler method?

Hello, I have a second order DE equation with 2 initial conditions. I have to solve it with Eurler's method but I don't kow how to do that in second order DE.

Is there anyone who can share a script or at least show me a way to do second order DE in euler method?

thanks a lot!

Answer 1

[Torsten]

g = 9.81;
L = 1.0;
T = 1.0;
dt = 0.01;
y_0 = pi/2;
v_0 = 0;

f = @(t,y)[y(2),-g/L*sin(y(1))];
t = (0:dt:T).';  
nt = numel(t);
node = 2;
y0 = [y_0 v_0];
y = zeros(nt,node)

y(1,:) = y0;
for it = 1:nt-1
    y(it+1,:) = y(it,:) + dt*f(t(it),y(it,:));
end
y_linear = v_0/sqrt(g/L)*sin(sqrt(g/L)*t) + y_0*cos(sqrt(g/L)*t);

plot(t,[y(:,1),y_linear])

But try to start earlier with your assignment next time. Or is it a challenge for you ?

[Onur Metin Mertaslan]

Thanks a lot, Actually I am totally new in matlab and it just given today, that's why I asked here :((