odes with variable coefficients

Question

harman singh 2015-3-18

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编辑： harman singh 2015-4-2

i am solving system of linear ode with time varying (gaussian )coefficients using standard ode45 approach but i am not getting desired results ,do i need to make some changes to accomodate time variartion of coefficients ? below i copy pasted from my m file along with command

    % function dy=tarak(t,y)
g0=.1;
t0=200;
s=90;
g=g0*exp(-((t-t0)/s).^2);%time varying gaussian coefficient "g"
G=sqrt(10);
dy=zeros(5,1);
dy(1)=-2*2*y(1)+1i*G*conj(y(3))+1i*g*conj(y(4))-1i*G*y(3)-1i*conj(g)*y(4);
dy(2)=2*y(1)+1i*G*y(3)-1i*G*conj(y(3));
dy(3)=-2*y(3)+1i*G*y(2)+1i*g*conj(y(5))-1i*G*y(1);
dy(4)=-2*y(4)+1i*G*y(5)+1i*g*(1-y(1)-y(2))-1i*g*y(1);
dy(5)=1i*G*y(4)-1i*g*conj(y(3));

Command [T,Y] = ode45(@tarak,[0 ,500],[0 0 0 0 0]);

Thanks for your time

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Answer 1

Torsten 2015-4-1

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Results.txt

Here are the results.

Best wishes

Torsten.

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Torsten 2015-4-1

dgl.txt

If you don't succeed, download "scilab" and execute the attached code.

Best wishes

Torsten.

harman singh 2015-4-2

编辑：harman singh 2015-4-2

hi Torsten , you were right by strengthening the tolerance level i am getting the much required positive results .

options = odeset('AbsTol', 1e-12); [T,Y] = ode45(@tarak, [0, 500], [0 0 1 0 0 0 0 0 0], options);

Thanks for your help .

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Answer 2

Torsten 2015-3-18

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Formally, everything looks fine. Of course we don't know if your underlying equations are correct.

Are you sure ODE45 can handle complex-valued ODEs ?

Best wishes

Torsten.

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harman singh 2015-3-23

编辑：harman singh 2015-3-23

在 MATLAB Online 中打开

"Are you sure ODE45 can handle complex-valued ODEs" ? hi i found this

 The ODE solvers in MATLAB 5 (R12) and later releases properly handle complex valued systems."MathWorks Support Team on 26 Jul 2010"

https://www.mathworks.com/matlabcentral/answers/102582-do-the-ode-functions-from-matlab-i-e-ode23-ode24-handle-complex-numbers-properly

harman singh 2015-4-1

在 MATLAB Online 中打开

hi Torsten, i have transformed my equations into real form

now these are 9 equations 
dy(1)=-2*2*y(1)+2*G*y(5)+2*g*y(7);
dy(2)=2*y(1)-2*G*y(5);
dy(3)=2*y(1)-2*g*y(7);
dy(4)=-2*y(4)+g*y(9);
dy(5)=-2*y(5)+G*(y(2)-y(1))+g*y(8);
dy(6)=-2*y(6)-G*y(9);
dy(7)=-2*y(7)+g*(y(3)-y(1))+G*y(8);
dy(8)=-G*y(7)-g*y(5);
dy(9)=G*y(6)-g*y(4);