Solving 3rd order ODE

Question

Kevin Tran 2020-5-10

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/524428-solving-3rd-order-ode

评论： Star Strider 2020-5-11

采纳的回答： Star Strider

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!

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Answer 1

Star Strider 2020-5-10

1
链接

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https://ww2.mathworks.cn/matlabcentral/answers/524428-solving-3rd-order-ode#answer_431612

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.

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Star Strider 2020-5-11

在 MATLAB Online 中打开

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.)