i want to plot coupled differential-algebraic equations dy/dt=Sqrt ((1-1/y^4)+log(y)) and z=Abs[(3*c​^2)*(4*e^2​)/((1-f^2/​((3*y^3)^2​))*4*(1 - f^2/(12*y^3))). Here c, e, f are constants and their values are known. What type of ode solver should i use.

 The initial value of y at t=0 is 1.005. Also the limits of t are 0 to 0.05.
I want the plot between z and t, also between y and t.

Answer 1

[Aykut Satici]

It seems like only the algebraic equation depends on the solution of the differential equation. Therefore, you can first solve the differential equation with a numerical integration routine, such as "ode45".

http://www.mathworks.com/help/matlab/ref/ode45.html

You can then use this solution to construct the dependent variable "z". Here is a script that does this:

par = [];
y0 = 1.005;
ti = 0; tf = 0.05;
opt = odeset('AbsTol',1.0e-07,'RelTol',1.0e-07);
[t,y] = ode45(@(t,y,par) sqrt( 1-1/y^4 + log(y) ), [ti,tf], y0 ,opt, par);

% The constants
c1 = 1;        % c
c2 = 2;        % e
c3 = 3;        % f

num = 12*c1^2*c2^2;
den = 4*( 1 - (c3^2)./(3*y.^3).^2 ).*( 1 - (c3^2)./(12*y.^3) );

z = abs( num./den );

% Visualize
f = figure(1); clf
subplot(2,1,1)
plot(t, y)
ylabel('y')
subplot(2,1,2)
plot(t, z)
xlabel('t')
ylabel('z')

[sv]

Thanks sir for your reply. Sir, I have made some changes in the above code according to my problem. But i am not getting any output. My code is function dd [t,y]=ode15s(@odefun,[0, 0.005],1.005); %plot(t,y(:,1),'-o') y(:,1) %grid end function dy =odefun(t,y) a=250; b= 1E+5; dy=sqrt((a*(1-(1/y(1))^4))+ b*log(y(1)));

c1 = 0.9965; c2 = 25.17*(10e-4);

num1 = c2; den1 =(1-(y.^3)/(4.201)); z = sqrt(c1+num1./den1); num2 =z.^2.* 0.0066; den2= 0.9996-z.^2; l=(num2./den2); num3=0.0014*(10e-4); den3=((1-4.2008/y.^3).^2.*(1-1.0502/y.^3)); c4 =0.00348; k=((num3./den3)+c4); eta=abs(l*k); % Visualize f = figure(1); clf axis([0,0.005,0,2]) %set the range of x and y subplot(2,1,1) plot(t, y(:,1)) ylabel('y') subplot(2,1,2) plot(t, eta) xlabel('t') ylabel('eta') grid end

In this code i want to use the values of y to plot a graph between eta and t. But i am not getting the plot. Kindly help me.

[Aykut Satici]

I am not sure what error you are getting, in particular. But you are probably looking for something like what I have attached.

My code may not be exactly what you want so please check.