MATLAB: solving a 2nd order ODE which has a parameter which evolves in time

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Mark Anslow 2020-2-23

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https://ww2.mathworks.cn/matlabcentral/answers/507132-matlab-solving-a-2nd-order-ode-which-has-a-parameter-which-evolves-in-time

评论： Star Strider 2020-2-24

Hi, I'm trying to solve the equation: y'' + k(t)y = 0 where k(t) is an array of values and y(0) = 1/2 and y'(0) = 1 in the range t = 0 to 20.

I understand it is possible to solve this as 2 coupled first order differential equations using ode45 as follows when k is constant:

k = 2

syms y(t)

[System] = odeToVectorField(diff(y, 2) == -(k).*y);

M = matlabFunction(System,'vars', {'t','Y'});

sol = ode45(M,[0 20],[1/2 1]);

fplot(@(x)deval(sol,x,1), [0, 20])

Please will you help me introduce the dependance on t of k(t), thanks!

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darova 2020-2-24

Please will you help me introduce the dependance on t of k(t), thanks!

Can you be more specific? What is it? Where is dependance?

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采纳的回答

Star Strider 2020-2-24

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/507132-matlab-solving-a-2nd-order-ode-which-has-a-parameter-which-evolves-in-time#answer_417122

在 MATLAB Online 中打开

Try this:

syms k(t) y(t)                                              % Declare ‘k(t)’ Here
[System,Subs] = odeToVectorField(diff(y, 2) == -(k).*y);    % Note ‘k(t)’ Included In Code
M = matlabFunction(System,'vars', {'t','Y'})
kv = rand(1,20);                                            % ‘k’ Vector
tv = linspace(0, 20, numel(kv));                            % Time Vector Matching ‘k’
k = @(t) interp1(tv, kv, t, 'linear', 'extrap');            % Function Interpolating ‘k’ To Specific Time
M = @(t,Y)[Y(2);-k(t).*Y(1)];                               % Output Of 'matlabFunction’ (Needs To Be Copied, And Pasted In The Code After The 'k' Function Is Defined)
[T,Y] = ode45(M,[0 20],[1/2 1]);
figure
plot(T, Y)
grid
xlabel('T')
ylabel('Amplitude')
legend(string(Subs))

Use your own ‘kv’ vector. The rest of the code should adapt to it, whatever it is.

oops guess i need help with reading skills. i saw a similar question before, where "k(t)" in the function sense was being confused with "k(t)" in the index sense. Hope this isn't one of those cases and one really needs the discretized time-dependence.

Star Strider 2020-2-24

Noted.

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