Using ODE45 to solve two coupled second order ODEs

Question

Ricardo Machado 2019-8-25

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/477472-using-ode45-to-solve-two-coupled-second-order-odes

回答： madhan ravi 2019-8-25

I used the ODE to vector field function to change my 2 coupled 2nd order ODEs to a system of 1st order ODEs.

 syms k1 k2 m t x1(t) x2(t) Y
Dx1 = diff(x1);
D2x1 = diff(x1,2);
Dx2 = diff(x2);
D2x2 = diff(x2,2);
Eq1 = D2x1 == (-(k1+k2)*x1+(k2)*x2)/m
Eq2 = D2x2 == ((k2*x1)+((k1+k2)*x2))/m
[V,Subs] = odeToVectorField(Eq1, Eq2)
ftotal = matlabFunction(V, 'Vars',{t,Y,k1,k2,m})

It generated this

ftotal =
  function_handle with value:
    @(t,Y,k1,k2,m)[Y(2);((k1+k2).*Y(1)+k2.*Y(3))./m;Y(4);-((k1+k2).*Y(3)-k2.*Y(1))./m]

However, when I tried to use ODE45 to solve it, i got errors. The initial conditions are x(0)= (1 0)' and ẋ(0)= (0 0)'

tspan = [0 20];
y0 = [1 0; 0 0];
[T,Y] = ode45(ftotal,tspan,y0)
plot(T,Y)
grid

Any help would be appreciated.

Thank you

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madhan ravi 2019-8-25

k1 , k2 and m values should be numeric.

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Answer 1

madhan ravi 2019-8-25

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/477472-using-ode45-to-solve-two-coupled-second-order-odes#answer_388931

在 MATLAB Online 中打开

syms x1(t) x2(t) k1 k2 m 
Dx1 = diff(x1);
D2x1 = diff(x1,2);
Dx2 = diff(x2);
D2x2 = diff(x2,2);
Eq1 = D2x1 == (-(k1+k2)*x1+(k2)*x2)/m;
Eq2 = D2x2 == ((k2*x1)+((k1+k2)*x2))/m;
[V,Subs] = odeToVectorField(Eq1, Eq2);
ftotal = matlabFunction(V, 'Vars',{'t','Y','k1','k2','m'});
%                                  ^-^ - single quotes
interval = [0 20];
y0 = [1 0; 0 0];     %initial conditions
%                                v-k2 
ySol = ode45( @(t,Y)ftotal(t,Y,1,1,1),interval,y0);
%                           k1-^ m-^
tValues = linspace(interval(1),interval(2),1000);
yValues = deval(ySol,tValues,1); %number 1 denotes first solution likewise you can mention 2 ,3 & 4 for the next three solutions
plot(tValues,yValues)