Error in solving second order diff eq. Error in odearguments

Question

Ketav Majumdar 2016-11-29

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https://ww2.mathworks.cn/matlabcentral/answers/314609-error-in-solving-second-order-diff-eq-error-in-odearguments

评论： Star Strider 2016-11-30

Hi, I am trying to solve a second order differential equation using ode15s and ode45. The are my scripts and driver files:

 Script
    % code
    %Mechanical Properties of Material
E=200e9; 
nu=0.3;
 %Constants A,B,C,D in the Equations
a11= (1/E);
a12= (-nu/E);
a33= (1/E);
A= (a12)/(a11+a12);
B= ((a33)-((2*a12^2)/(a11+a12)));
C= (a11)/(a11.^2-a12.^2);
D= (2*a12+a11)/(a11+a12);
 %Finding Sigma_rr
O =(D+B*C-A*D);
M = A-2;
function Sigma_rr = Euler_Cauchy(t,y)
Sigma_rr = [y(2); (1/t)*(M*y(2)+O*y)];
end

and

driver file
  % tspan = [1 1.2];
y0 = [100000000, 0];
[t,y] = ode15s(@Sigma_rr, tspan, y0);
plot(t,y(:,1))
figure
plot(t,y(:,2))
end

I get the following error message

 Error in odearguments (line 90)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.
 Error in ode15s (line 150)
    odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);
 Error in IsotropicThickWallCylinderPlot (line 3)
[t,y] = ode15s(@Sigma_rr, tspan, y0);

I have been on the forums here but have had no luck in figuring out whats wrong. I have terrible matlab skills so any help will be much appreciated.

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Answer 1

Star Strider 2016-11-29

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https://ww2.mathworks.cn/matlabcentral/answers/314609-error-in-solving-second-order-diff-eq-error-in-odearguments#answer_245237

在 MATLAB Online 中打开

You have two errors:

Your function is ‘Euler_Cauchy’, not ‘Sigma_rr’, and since ‘Sigma_rr’ variable is local only to the function, so it doesn’t exist in your workspace;
The ‘y’ argument is a (2x1) vector so you need to substitute ‘y(1)’ for ‘y’ in the second row in your ODE function matrix (since I assume that is what you intended).

This works:

%Constants A,B,C,D in the Equations
a11= (1/E);
a12= (-nu/E);
a33= (1/E);
A= (a12)/(a11+a12);
B= ((a33)-((2*a12^2)/(a11+a12)));
C= (a11)/(a11.^2-a12.^2);
D= (2*a12+a11)/(a11+a12);
   %Finding Sigma_rr
  O =(D+B*C-A*D);
  M = A-2;
  Euler_Cauchy = @(t,y) [y(2); (1/t)*(M*y(2)+O*y(1))];
tspan = [1 1.2];
y0 = [100000000, 0];
[t,y] = ode15s(Euler_Cauchy, tspan, y0);
plot(t,y(:,1))
figure
plot(t,y(:,2))

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Ketav Majumdar 2016-11-30

ok that solved the issue! thank you very much. However, i believe there has been an error in the way the boundary conditions have been specified.

The boundary conditions given are:

y(1)=-100E6; y(1.2)=0;

Ive looked around however the matlab documents only give a case where the boundary conditions are for y and y'. Any suggestions?

Star Strider 2016-11-30

My pleasure.

The ode15s solver is for stiff initial-value problems. For boundary value problems, you need bvp4c or bvp5c. I have limited experience with them (and none recent), so I can’t suggest code for a specific solution.

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