At 49:00 - The mistake is on line 41: you need to address the array asol with two indices: asol(j,1) and asol(j,2) . Otherwise you get the result with fixed a(0) amplitudes for the modes, that is, the solution doesn't change over time. Too bad you didn't notice- I was looking forward to see how well it works. But I must say this was a really good impromptu explanations and demos. I really enjoyed it, and learned a lot. Thanks.
I have a question. here i know about the modal energy and specific modes i.e. 1st mode or 2nd mode etc. here 1st mode means (1,1) i.e the position of the mode?
hahaha, I believe the error was that you actually have to compute the innerproduct. Try numerical integration such as: a1=sum(mode1.*2sech)*L/Nx and a2=sum(mode2.*2sech)*L/Nx. You where so close to a correct code. But otherwise, this was a great series of lectures.
Very nice explanation but i have a question. What if you have for example a system of 100 states with 100 different nonlinear ordinary differential equations ? How would you solve the Galerkin projection ? You take each differential equation and solve it separately like it is done in the video ? Please help
Thanks. Would it be for j=1:length(t) usol(j,:)=asol(j)*phi(:,1)+asol(j)*phi(:,2); end It seems like the surfl result from this looks like what could be a 2-mode approx.
I think it'd be more like: for j = 1:length(t) usol(j,:) = asol(j,1)*phi(:,1) + asol(j,2)*phi(:,2) end Because you want to compute the following at each time j: u = a1*psi1 + a2*psi2 and asol has 2 columns in this case of a 2 mode rom
At 49:00 - The mistake is on line 41: you need to address the array asol with two indices: asol(j,1) and asol(j,2) . Otherwise you get the result with fixed a(0) amplitudes for the modes, that is, the solution doesn't change over time. Too bad you didn't notice- I was looking forward to see how well it works. But I must say this was a really good impromptu explanations and demos. I really enjoyed it, and learned a lot. Thanks.
It was amazing, thanks professor🌹
May I know why k isn't defined as 2*pi/L ( - n/2 : n/2 -1 ) ?
I have a question. here i know about the modal energy and specific modes i.e. 1st mode or 2nd mode etc. here 1st mode means (1,1) i.e the position of the mode?
Sir, Nice lecture.
Can you suggest me some problems or project?
Can you please post the link of course page where you'll be posting the updated code.
Thanks.
hahaha, I believe the error was that you actually have to compute the innerproduct. Try numerical integration such as: a1=sum(mode1.*2sech)*L/Nx and a2=sum(mode2.*2sech)*L/Nx. You where so close to a correct code. But otherwise, this was a great series of lectures.
Very nice explanation but i have a question. What if you have for example a system of 100 states with 100 different nonlinear ordinary differential equations ? How would you solve the Galerkin projection ? You take each differential equation and solve it separately like it is done in the video ? Please help
The error comes in the for loop that makes usol. You need to get the asol at each time step not just the first and second ones
Thanks. Would it be
for j=1:length(t)
usol(j,:)=asol(j)*phi(:,1)+asol(j)*phi(:,2);
end
It seems like the surfl result from this looks like what could be a 2-mode approx.
I think it'd be more like:
for j = 1:length(t)
usol(j,:) = asol(j,1)*phi(:,1) + asol(j,2)*phi(:,2)
end
Because you want to compute the following at each time j:
u = a1*psi1 + a2*psi2
and asol has 2 columns in this case of a 2 mode rom