0 个投票

Hi guys, I need to solve this 3rd order ODE:
?⃛+2??̈+3??̇+4??=2, t≥0, ?̈(0)=?̇(0)=?(0)=0
This is my script:
[t,y] = ode45(@diffeq3,[0 50],[0;-1;1]);
plot(t,y)
function dy = diffeq3(t,y)
if t >= 0
dy(3) = 0
dy(2) = 0
dy(1) = 0
end
dy = zeros(3,1);
dy(1) = y(2);
dy(2) = y(3);
dy(3) = 2 - 2*y(3) - 3*y(2) - 4*y(1);
end
Did I do it right?
I got two questions, I got three curves which on is which?
And did I define t≥0, ?̈(0)=?̇(0)=?(0)=0 correct? With:
if t >= 0
dy(3) = 0
dy(2) = 0
dy(1) = 0
Thanks in advance for the help!

请先登录，再回答此问题。

 采纳的回答

Star Strider
Star Strider 2020-5-10

1 个投票

There appears to be a factor of ‘y(1)’ missing in the last 3 terms of the ‘dy(3)’ equation. (I gave your differential equation as posted to the odeToVectorField function to be certain.)
Also, the if block is not necessary. It does nothing, and produces slower code.

6 个评论
显示 4更早的评论 隐藏 4更早的评论

Kevin Tran
Kevin Tran 2020-5-10
Sorry when I pasted in the equation something happened, it should be ?⃛+2?̈+3?̇+4?=2
This is the new script I made from your suggestion:
[t,y] = ode45(@diffeq3,[0 50],[0;-1;1]);
plot(t,y)
function dydt = diffeq3(t,y)
dydt = zeros(3,1);
dydt(1) = y(2);
dydt(2) = y(3);
dydt(3) = 2 - 2*y(3) - 3*y(2) - 4*y(1);
end
From what you wrote I take it as you don't have to define t≥0, ?̈(0)=?̇(0)=?(0)=0 and it does so automatically?
Also I get 3 curves and have no idea which one is which and would really appreciate the help. I'm really new to this with matlab and I'm still confused with ODE and how the graph it produces should look.
Also thanks for the help in advance!
Star Strider
Star Strider 2020-5-11
The function appears to be correct.
‘From what you wrote I take it as you don't have to define t≥0, ?̈(0)=?̇(0)=?(0)=0 and it does so automatically?’
Yes. The ODE integration functions (ode45 here) take the initial conditions as the third argument, so it is not only not necessary to define them inside the ODE function, it is not appropriate to do so.
‘Also I get 3 curves and have no idea which one is which and would really appreciate the help.’
The curves appear in to order in which they appear in the differential equation vector, so here, y, , and in order. The symbolic Math Toolbox takes care of these in the odeToVectorField function, so use the second output and the string function to create a legend argument that will display them correctly:
syms y(t) t Y
D1y = diff(y);
D2y = diff(y,2);
D3y = diff(y,3);
Eq = D3y + 2*D2y + 3*D1y + 4*y == 2;
[VF,Subs] = odeToVectorField(Eq)
diffeq3 = matlabFunction(VF, 'Vars',{t,Y})
[t,y] = ode45(diffeq3,[0 50],[0;-1;1]);
plot(t,y)
legend(string(Subs))
producing:
I prefer this because the Symbolic Math Toolbox does not make the typical algebra errors that I frequently do. Also this is MATLAB Answers, so I use it frequently to derive such functions and expressions. (It saves me time and embarrassment.)
Kevin Tran
Kevin Tran 2020-5-11
Thank you so much and for taking the time explaining everything. I seem to get the hang of it now which really makes using matlab more enjoyable.
By the way I think ?̈(0)=?̇(0)=?(0)=0 meaning all the curves should start from 0 which can be defined by setting:
[t,y] = ode45(diffeq3,[0 50],[0;0;0]);
instead of
[t,y] = ode45(diffeq3,[0 50],[0;-1;1]);
and this is my final code, (got a little help with legend from another user). Looking perfect now?
[t,y] = ode45(@diffeq3,[0 50],[0;0;0]);
plot(t,y)
legend({'y(t)', '$\dot{y}(t)$', '$\ddot{y}(t)$'}, 'Interpreter', 'latex')
function dy = diffeq3(t,y)
dy = zeros(3,1);
dy(1) = y(2);
dy(2) = y(3);
dy(3) = 2 - 2*y(3) - 3*y(2) - 4*y(1);
end
Star Strider
Star Strider 2020-5-11
It looks good to me!
‘got a little help with legend from another user’
I saw that. I could have helped you with it, since I did the same in my previous Comment.
Kevin Tran
Kevin Tran 2020-5-11
Yeah just different ways of writing the script, thanks for all the help by the way!
Star Strider
Star Strider 2020-5-11
As always, my pleasure!

请先登录，再进行评论。

更多回答（0 个）

类别

在 帮助中心 和 File Exchange 中查找有关 Programming 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by