Solving second order non-linear equations (time-domain)

Question

Jake 2020-8-10

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/577621-solving-second-order-non-linear-equations-time-domain

编辑： Alan Stevens 2020-8-11

Hi everyone,

Im starting to learn ODE solving using MATLAB. I'm new to this, although I'm fairly comfortable using MATLAB. (I'm learning alone, as I go)

So, I want to solve an equation like the following one, and basically hoping to have a simulation (sort of) output as a plot. How do I approach this?

I'm posting this in advance and I will be looking for resources and other references after posting this :) Again, I'm not sure how to approach this and frankly, I'm not sure how to solve the equation itself.

Apologies for the broad question. Any pointer or lead will be highly appreciated, in a learning point of view.

Thanks in advance!

3 个评论
显示 1更早的评论隐藏 1更早的评论

Jake 2020-8-11

Thank you so much for the response!

Although I'm not familiar with the Symbolic toolbox, I'm fairly good with Simulink. I think I will try that. I understand that I have to study the math as well as solving it using MATLAB :) I was digging through the books too.

> if you have any questions regarding these,

I'm not sure if you were going to add some links here. I'd love to see some references though, if you have ay recommendations :)

Thank you again!

hosein Javan 2020-8-11

you're welcome.

regarding reference book: "differential equations, boyce and diprima"

you can solve either by homogeneous and particular solutions of second-order ode or by using laplace transform.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Alan Stevens 2020-8-10

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/577621-solving-second-order-non-linear-equations-time-domain#answer_477667

编辑：Alan Stevens 2020-8-11

Here's the basic idea. First turn your second-order ODE into twofirst order ones, like so:

Then structure your code along the following lines:

P0 = [phi0  v0];  % Initial values of phi and v
tspan = [0 tend]; % Time over which to integrate
[t, P] = ode45(@phidot, tspan, P0);  % Call ode solver
phi = P(:,1); % Extract values of phi
plot(t,phi)  % plot results
% Function
function dphidt = phidot(t,P)
 % Enter data needed e.g. omega4 = etc.
  
 phi = P(1);
 v = P(2);
 
 dphidt = [v;
           -2nv - wn4^2*phi + etc.];
 
end

Obviously the above coding is sketchy, but hopefully it's enough to give you the general idea.

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Jake 2020-8-11

编辑：Jake 2020-8-11

This makes a lot of sense. I hope I will be able to figure out the complete code soon, after referring to other notes and sources. Thank you so much for taking your time for this :) Means alot!

请先登录，再进行评论。