ODE45 requires more parameters than it should

Hello All,

I am solving a parametric systems of ODEs in Matlab. I have defined 11 parameters in matlabfunction command, but when it comes to use the ode45 command it requires 14 parameters.

syms m A alpha theta(t) b u(t) I B n J x(t) y(t) D c cr  %J=Ir
X=A*sin(alpha*t)
phi=B*sin(n*alpha*t)   
%D=c*(diff(x)*cos(theta)+diff(y)*sin(theta))/2+cr*theta^2/2
lambda= m*(I+J)*(-2*diff(X,2)*sin(theta)+u*diff(theta)-(b*(J*diff(phi,2)+cr*diff(theta))/(I + J)))/(I+J+m*b^2)
ode1= diff(theta,2) == -(lambda*b+J*diff(phi,2)+cr*diff(theta))/(I+J)
ode2= diff(u)       == -c*u/m+diff(theta)^2*b-2*diff(X,2)*cos(theta)
[V] = odeToVectorField(ode1,ode2)
M = matlabFunction(V,'vars', {'t','Y','A','I','alpha','b','m','B','J','n','c','cr'})
IC = [0 0 0]  % Init conds for u , theta, thetadot
tspan_solve=0:0.1:20
tspan_plot=[0 20];
sol = ode45(M,tspan_solve,IC,1,0.00001,1,1,1,1,0.1,1,1,100,100) % Parameters for A, I, alpha, b, m, B, J, n, c, cr

I changed that first parameters and it seemed that has no effect on the solution, but still need to make sure what that is and fix this issue. Every time I try to change the parameters and see the results I get confused.

[Torsten]

Use

M = matlabFunction(V)

to see which parameters are included in your equations.

After this, you can arrange them as you like.

[ali mohseni]

I did so. Still matlabFunction has 12 parameters which are as follows:

M = function_handle with value:

@(A,B,I,J,Y,alpha,b,c,cr,m,n,t)[b.*Y(3).^2-(c.*Y(1))./m+A.*alpha.^2.*cos(Y(2)).*sin(alpha.*t).*2.0;Y(3);-(cr.*Y(3)-B.*J.*alpha.^2.*n.^2.*sin(alpha.*n.*t)+(b.*m.*(I+J).*(Y(1).*Y(3)-(b.*(cr.*Y(3)-B.*J.*alpha.^2.*n.^2.*sin(alpha.*n.*t)))./(I+J)+A.*alpha.^2.*sin(Y(2)).*sin(alpha.*t).*2.0))./(I+J+b.^2.*m))./(I+J)]

but ode45 requires 13 output in the code above. The inputs to ode45 are

tspan_solve,IC,1,0.00001,1,1,1,1,0.1,1,1,100,100.

Answer 1

[Cris LaPierre]

The first 2 inputs to your function must by t and y, which they are. Those correspond to tspan_solve and IC. The remaining input arguments must come after all other inputs for ode45 have been entered, including options.

• [t,y] = ode45(odefun,tspan,y0,options)

It would appear your input A does not have much of an impact on the results.

syms m A alpha theta(t) b u(t) I B n J x(t) y(t) D c cr K X(t)%J=Ir
phi=B*sin(n*alpha*t);
%D=c*(diff(x)*cos(theta)+diff(y)*sin(theta))/2+cr*theta^2/2
lambda= m*(I+J)*(-2*diff(X,2)*sin(theta)+u*diff(theta)-(b*(J*diff(phi,2)+cr*diff(theta))/(I + J)))/(I+J+m*b^2);
ode1= diff(theta,2) == -(lambda*b+J*diff(phi,2)+cr*diff(theta))/(I+J);
ode2= diff(u)       == -c*u/m+diff(theta)^2*b-2*diff(X,2)*cos(theta);
ode3= diff(X,2)     == 2*lambda*sin(theta)+c*u*cos(theta)-2*K*X;
[V] = odeToVectorField(ode1,ode2,ode3);
M = matlabFunction(V,'vars', {'t','Y','A','I','alpha','b','m','B','J','n','c','cr','K'})

M = function_handle with value:
    @(t,Y,A,I,alpha,b,m,B,J,n,c,cr,K)[Y(2);(I.*K.*Y(1).*-2.0-J.*K.*Y(1).*2.0-K.*b.^2.*m.*Y(1).*2.0+I.*c.*cos(Y(3)).*Y(5)+J.*c.*cos(Y(3)).*Y(5)-b.*cr.*m.*sin(Y(3)).*Y(4).*2.0+I.*m.*sin(Y(3)).*Y(4).*Y(5).*2.0+J.*m.*sin(Y(3)).*Y(4).*Y(5).*2.0+b.^2.*c.*m.*cos(Y(3)).*Y(5)+B.*J.*alpha.^2.*b.*m.*n.^2.*sin(alpha.*n.*t).*sin(Y(3)).*2.0)./(I+J+b.^2.*m+I.*m.*sin(Y(3)).^2.*4.0+J.*m.*sin(Y(3)).^2.*4.0);Y(4);-(cr.*Y(4)+cr.*m.*sin(Y(3)).^2.*Y(4).*4.0+b.*m.*Y(4).*Y(5)+K.*b.*m.*sin(Y(3)).*Y(1).*4.0-B.*J.*alpha.^2.*n.^2.*sin(alpha.*n.*t)-b.*c.*m.*cos(Y(3)).*sin(Y(3)).*Y(5).*2.0-B.*J.*alpha.^2.*m.*n.^2.*sin(alpha.*n.*t).*sin(Y(3)).^2.*4.0)./(I+J+b.^2.*m+I.*m.*sin(Y(3)).^2.*4.0+J.*m.*sin(Y(3)).^2.*4.0);-(-b.^3.*m.^2.*Y(4).^2+I.*c.*Y(5)+J.*c.*Y(5)-I.*b.*m.*Y(4).^2-J.*b.*m.*Y(4).^2+b.^2.*c.*m.*Y(5)-K.*b.^2.*m.^2.*cos(Y(3)).*Y(1).*4.0-I.*K.*m.*cos(Y(3)).*Y(1).*4.0-J.*K.*m.*cos(Y(3)).*Y(1).*4.0-I.*b.*m.^2.*sin(Y(3)).^2.*Y(4).^2.*4.0-J.*b.*m.^2.*sin(Y(3)).^2.*Y(4).^2.*4.0+b.^2.*c.*m.^2.*cos(Y(3)).^2.*Y(5).*2.0+I.*c.*m.*cos(Y(3)).^2.*Y(5).*2.0+J.*c.*m.*cos(Y(3)).^2.*Y(5).*2.0+I.*c.*m.*sin(Y(3)).^2.*Y(5).*4.0+J.*c.*m.*sin(Y(3)).^2.*Y(5).*4.0+I.*m.^2.*cos(Y(3)).*sin(Y(3)).*Y(4).*Y(5).*4.0+J.*m.^2.*cos(Y(3)).*sin(Y(3)).*Y(4).*Y(5).*4.0-b.*cr.*m.^2.*cos(Y(3)).*sin(Y(3)).*Y(4).*4.0+B.*J.*alpha.^2.*b.*m.^2.*n.^2.*sin(alpha.*n.*t).*cos(Y(3)).*sin(Y(3)).*4.0)./(m.*(I+J+b.^2.*m+I.*m.*sin(Y(3)).^2.*4.0+J.*m.*sin(Y(3)).^2.*4.0))]

IC = [0 0 0 1 1];  % Init conds for u , theta, thetadot, X, Xdot
tspan_solve=0:0.1:100;
tspan_plot=[0 100];

sol = ode45(M,tspan_solve,IC,[],1,5,1,1,1,1,1,1,1,1,1); % Parameters for A, I, alpha, b, m, B, J, n, c, cr
%                            ^^   ^   my changes
plot(sol.x,sol.y(1,:))

[ali mohseni]

I know that in this case the A has no effect on the odes, but still ode45 requires one extra parameters. so here I just deleted extra parameters like A and n to make the code more tidy. As you can see, now I have 11 parameters defined in matlabFunction but ode45 works only with 12 inputs.

syms m alpha theta(t) b u(t) I B J x(t) y(t) D c cr K X(t)%J=Ir
phi=B*sin(alpha*t);
lambda= m*(I+J)*(-2*diff(X,2)*sin(theta)+u*diff(theta)-(b*(J*diff(phi,2)+cr*diff(theta))/(I + J)))/(I+J+m*b^2);
ode1= diff(theta,2) == -(lambda*b+J*diff(phi,2)+cr*diff(theta))/(I+J);
ode2= diff(u)       == -c*u/m+diff(theta)^2*b-2*diff(X,2)*cos(theta);
ode3= diff(X,2)     == 2*lambda*sin(theta)+c*u*cos(theta)-2*K*X;
[V] = odeToVectorField(ode1,ode2,ode3);
M = matlabFunction(V,'vars', {'t','Y','I','alpha','b','m','B','J','c','cr','K'})

M = function_handle with value:
    @(t,Y,I,alpha,b,m,B,J,c,cr,K)[Y(2);(I.*K.*Y(1).*-2.0-J.*K.*Y(1).*2.0-K.*b.^2.*m.*Y(1).*2.0+I.*c.*cos(Y(3)).*Y(5)+J.*c.*cos(Y(3)).*Y(5)-b.*cr.*m.*sin(Y(3)).*Y(4).*2.0+I.*m.*sin(Y(3)).*Y(4).*Y(5).*2.0+J.*m.*sin(Y(3)).*Y(4).*Y(5).*2.0+b.^2.*c.*m.*cos(Y(3)).*Y(5)+B.*J.*alpha.^2.*b.*m.*sin(Y(3)).*sin(alpha.*t).*2.0)./(I+J+b.^2.*m+I.*m.*sin(Y(3)).^2.*4.0+J.*m.*sin(Y(3)).^2.*4.0);Y(4);-(cr.*Y(4)-B.*J.*alpha.^2.*sin(alpha.*t)+cr.*m.*sin(Y(3)).^2.*Y(4).*4.0+b.*m.*Y(4).*Y(5)+K.*b.*m.*sin(Y(3)).*Y(1).*4.0-B.*J.*alpha.^2.*m.*sin(Y(3)).^2.*sin(alpha.*t).*4.0-b.*c.*m.*cos(Y(3)).*sin(Y(3)).*Y(5).*2.0)./(I+J+b.^2.*m+I.*m.*sin(Y(3)).^2.*4.0+J.*m.*sin(Y(3)).^2.*4.0);-(-b.^3.*m.^2.*Y(4).^2+I.*c.*Y(5)+J.*c.*Y(5)-I.*b.*m.*Y(4).^2-J.*b.*m.*Y(4).^2+b.^2.*c.*m.*Y(5)-K.*b.^2.*m.^2.*cos(Y(3)).*Y(1).*4.0-I.*K.*m.*cos(Y(3)).*Y(1).*4.0-J.*K.*m.*cos(Y(3)).*Y(1).*4.0-I.*b.*m.^2.*sin(Y(3)).^2.*Y(4).^2.*4.0-J.*b.*m.^2.*sin(Y(3)).^2.*Y(4).^2.*4.0+b.^2.*c.*m.^2.*cos(Y(3)).^2.*Y(5).*2.0+I.*c.*m.*cos(Y(3)).^2.*Y(5).*2.0+J.*c.*m.*cos(Y(3)).^2.*Y(5).*2.0+I.*c.*m.*sin(Y(3)).^2.*Y(5).*4.0+J.*c.*m.*sin(Y(3)).^2.*Y(5).*4.0+I.*m.^2.*cos(Y(3)).*sin(Y(3)).*Y(4).*Y(5).*4.0+J.*m.^2.*cos(Y(3)).*sin(Y(3)).*Y(4).*Y(5).*4.0-b.*cr.*m.^2.*cos(Y(3)).*sin(Y(3)).*Y(4).*4.0+B.*J.*alpha.^2.*b.*m.^2.*cos(Y(3)).*sin(Y(3)).*sin(alpha.*t).*4.0)./(m.*(I+J+b.^2.*m+I.*m.*sin(Y(3)).^2.*4.0+J.*m.*sin(Y(3)).^2.*4.0))]

IC = [0 0 0 1 1];  % Init conds for u , theta, thetadot, X, Xdot;
tspan_solve=0:0.1:100;
tspan_plot=[0 100];
sol = ode45(M,tspan_solve,IC,1,1,1,1,1,1,1,1,1,1) % Parameters for I, alpha, b,  m, B, J, c, cr, K

sol = struct with fields:
     solver: 'ode45'
    extdata: [1×1 struct]
          x: [0 2.0095e-04 0.0012 0.0062 0.0313 0.1539 0.3730 0.6942 1.1139 1.7977 2.4751 3.1526 3.7802 4.3105 4.9130 5.5156 6.0510 6.5580 7.1590 7.7309 8.4067 8.7822 9.1577 9.4928 9.8279 10.2876 10.6589 11.2264 11.8542 12.4819 13.0872 13.6235 … ]
          y: [5×248 double]
      stats: [1×1 struct]
      idata: [1×1 struct]

[Cris LaPierre]

You do not need to add an extra parameter. You do need to be aware of the expected inputs. I think your 'extra' parameter is being interpretted as the options input, as I pointed out previously.

Sticking with the syntax you are using, your inputs should be

sol = ode45(odefun,tspan, y0,options,...) or

sol = ode45(M, tspan_solve,IC,options,I,alpha,b,m,B,J,c,cr,K)

syms m alpha theta(t) b u(t) I B J x(t) y(t) D c cr K X(t)%J=Ir
phi=B*sin(alpha*t);
lambda= m*(I+J)*(-2*diff(X,2)*sin(theta)+u*diff(theta)-(b*(J*diff(phi,2)+cr*diff(theta))/(I + J)))/(I+J+m*b^2);
ode1= diff(theta,2) == -(lambda*b+J*diff(phi,2)+cr*diff(theta))/(I+J);
ode2= diff(u)       == -c*u/m+diff(theta)^2*b-2*diff(X,2)*cos(theta);
ode3= diff(X,2)     == 2*lambda*sin(theta)+c*u*cos(theta)-2*K*X;
[V] = odeToVectorField(ode1,ode2,ode3);
M = matlabFunction(V,'vars', {'t','Y','I','alpha','b','m','B','J','c','cr','K'})

M = function_handle with value:
    @(t,Y,I,alpha,b,m,B,J,c,cr,K)[Y(2);(I.*K.*Y(1).*-2.0-J.*K.*Y(1).*2.0-K.*b.^2.*m.*Y(1).*2.0+I.*c.*cos(Y(3)).*Y(5)+J.*c.*cos(Y(3)).*Y(5)-b.*cr.*m.*sin(Y(3)).*Y(4).*2.0+I.*m.*sin(Y(3)).*Y(4).*Y(5).*2.0+J.*m.*sin(Y(3)).*Y(4).*Y(5).*2.0+b.^2.*c.*m.*cos(Y(3)).*Y(5)+B.*J.*alpha.^2.*b.*m.*sin(Y(3)).*sin(alpha.*t).*2.0)./(I+J+b.^2.*m+I.*m.*sin(Y(3)).^2.*4.0+J.*m.*sin(Y(3)).^2.*4.0);Y(4);-(cr.*Y(4)-B.*J.*alpha.^2.*sin(alpha.*t)+cr.*m.*sin(Y(3)).^2.*Y(4).*4.0+b.*m.*Y(4).*Y(5)+K.*b.*m.*sin(Y(3)).*Y(1).*4.0-B.*J.*alpha.^2.*m.*sin(Y(3)).^2.*sin(alpha.*t).*4.0-b.*c.*m.*cos(Y(3)).*sin(Y(3)).*Y(5).*2.0)./(I+J+b.^2.*m+I.*m.*sin(Y(3)).^2.*4.0+J.*m.*sin(Y(3)).^2.*4.0);-(-b.^3.*m.^2.*Y(4).^2+I.*c.*Y(5)+J.*c.*Y(5)-I.*b.*m.*Y(4).^2-J.*b.*m.*Y(4).^2+b.^2.*c.*m.*Y(5)-K.*b.^2.*m.^2.*cos(Y(3)).*Y(1).*4.0-I.*K.*m.*cos(Y(3)).*Y(1).*4.0-J.*K.*m.*cos(Y(3)).*Y(1).*4.0-I.*b.*m.^2.*sin(Y(3)).^2.*Y(4).^2.*4.0-J.*b.*m.^2.*sin(Y(3)).^2.*Y(4).^2.*4.0+b.^2.*c.*m.^2.*cos(Y(3)).^2.*Y(5).*2.0+I.*c.*m.*cos(Y(3)).^2.*Y(5).*2.0+J.*c.*m.*cos(Y(3)).^2.*Y(5).*2.0+I.*c.*m.*sin(Y(3)).^2.*Y(5).*4.0+J.*c.*m.*sin(Y(3)).^2.*Y(5).*4.0+I.*m.^2.*cos(Y(3)).*sin(Y(3)).*Y(4).*Y(5).*4.0+J.*m.^2.*cos(Y(3)).*sin(Y(3)).*Y(4).*Y(5).*4.0-b.*cr.*m.^2.*cos(Y(3)).*sin(Y(3)).*Y(4).*4.0+B.*J.*alpha.^2.*b.*m.^2.*cos(Y(3)).*sin(Y(3)).*sin(alpha.*t).*4.0)./(m.*(I+J+b.^2.*m+I.*m.*sin(Y(3)).^2.*4.0+J.*m.*sin(Y(3)).^2.*4.0))]

opts = [];
IC = [0 0 0 1 1];  % Init conds for u , theta, thetadot, X, Xdot;
tspan_solve=0:0.1:100;
tspan_plot=[0 100];
sol = ode45(M,tspan_solve,IC,opts,1,1,1,1,1,1,1,1,1); % Parameters for I, alpha, b,  m, B, J, c, cr, K

plot(sol.x,sol.y(1,:))

Answer 2

[Steven Lord]

That syntax, where you pass additional input arguments after the options structure, is an older syntax that is no longer documented and is intended for backwards compatibility.

Instead I recommend using one of the techniques described in the Parameterizing Functions link in the description of the odefun input argument on the ode45 documentation page. There's also an example on the ode45 documentation page that demonstrates the technique; see "Pass Extra Parameters to ODE Function" on that page.

Answer 3

[Walter Roberson]

Change

M = matlabFunction(V,'vars', {'t','Y','A','I','alpha','b','m','B','J','n','c','cr'})

to

M = matlabFunction(V, 'vars', {[t Y A I alpha b m B J n c cr]})

[ali mohseni]

How that works?

Do you mean I pass my input to parameters in the matlabFunction instead of doing that in ode45?