Functions close to zero in MATLAB

[Juggler123]

Hi all,

I need to find where a collection of curves are all approximately equal to zero (given some tolerance level) and was wondering if anyone could help me?

I'm running the following script in MATLAB:

dF2=0.001;
dG2=0.001;
initF2=0.522;
initG2=-0.603;
K=zeros(2);
etaspan=[0 20];
H=[1;1];
options=odeset('AbsTol',1e-7,'RelTol',1e-4);
while max(abs(H))>1e-8
[eta,X]=ode45(@nN,etaspan,[0;initF2+dF2;1;initG2;0],options);
n=size(eta,1);
X2=[X(n,1);X(n,3)];
[eta,X]=ode45(@nN,etaspan,[0;initF2;1;initG2+dG2;0],options);
n=size(eta,1);
X3=[X(n,1);X(n,3)];
[eta,X]=ode45(@nN,etaspan,[0;initF2;1;initG2;0],options);
n=size(eta,1);
X1=[X(n,1);X(n,3)];
K(1,1)=(X2(1)-X1(1))/dF2;
K(2,1)=(X2(2)-X1(2))/dF2;
K(1,2)=(X3(1)-X1(1))/dG2;
K(2,2)=(X3(1)-X1(2))/dG2;
H=K\-X1;
initF2=initF2+H(1);
initG2=initG2+H(2);
end

figure;
hold all;
plot(eta,X(:,1));
plot(eta,X(:,3));
plot(eta,(-1)*X(:,5));
plot(eta,X(:,2));
plot(eta,X(:,4));
hold off;
xlabel('\eta')
hleg = legend('F','G','-H','F\prime','G\prime','Location','SouthEast');

disp('Value of F''(0)')
a = X(1,2);
disp(a)

disp('Value of G''(0)')
b = X(1,4);
disp(b)

disp('Value of H(20)')
c = X(end,5);
disp(c)


Calling the function:


function Y=nN(x,X)

n=1.3;

dF1deta=X(2);

dF2deta=n^(-1)*((X(2)^(2)+X(4)^(2))^((n-1)/2))^(-1)*((X(1)^(2)-X(3)^(2)+(X(5)+((1-n)/(n+1))*X(1)*x)*X(2))*(1+(n-1)*(X(2)^(2)+X(4)^2)^(-1)*X(4)^(2))-(n-1)*X(2)*X(4)*(X(2)^(2)+X(4)^(2))^(-1)*(2*X(1)*X(3)+(X(5)+((1-n)/(n+1))*X(1)*x)*X(4)));

dG1deta=X(4);

dG2deta=n^(-1)*((X(2)^(2)+X(4)^(2))^((n-1)/2))^(-1)*((2*X(1)*X(3)+(X(5)+((1-n)/(n+1))*X(1)*x)*X(4))*(1+(n-1)*(X(2)^(2)+X(4)^2)^(-1)*X(2)^(2))-(n-1)*X(2)*X(4)*(X(2)^(2)+X(4)^(2))^(-1)*(X(1)^(2)-X(3)^(2)+(X(5)+((1-n)/(n+1))*X(1)*x)*X(2)));

dH1deta=-2*X(1)-(1-n)/(n+1)*x*X(2);

Y = [dF1deta; dF2deta; dG1deta; dG2deta; dH1deta];


From the plot that is produced I would like to find where the curves for F, F', G and G' are approximately equal to zero given a tolerance of 1e-6. Simply from looking at the plot I can see that this is around eta~5.7 but I would like to be able to print out this value of eta.

Is this possible?

Any help would be greatly appreciated.

 

[mmwave]

Hi there,

It looks like your code is solving a system of differential equations using the ode45 function in MATLAB. In order to find where the curves are approximately equal to zero, you can use the find function in MATLAB. This function will return the indices of the elements in a vector that meet a certain condition. In your case, you can use it to find the indices where the values of F, F', G, and G' are less than the tolerance level of 1e-6. Then, you can use these indices to find the corresponding values of eta using the eta vector from your ode45 function. Here is an example of how you could do this:

% Find the indices where the values of F, F', G, and G' are less than the tolerance level
indF = find(abs(X(:,1)) < 1e-6);
indFprime = find(abs(X(:,2)) < 1e-6);
indG = find(abs(X(:,3)) < 1e-6);
indGprime = find(abs(X(:,4)) < 1e-6);

% Find the corresponding values of eta
etaF = eta(indF);
etaFprime = eta(indFprime);
etaG = eta(indG);
etaGprime = eta(indGprime);

% Print out the values of eta where the curves are approximately equal to zero
disp('Value of eta where F is approximately equal to zero:')
disp(etaF)
disp('Value of eta where F'' is approximately equal to zero:')
disp(etaFprime)
disp('Value of eta where G is approximately equal to zero:')
disp(etaG)
disp('Value of eta where G'' is approximately equal to zero:')
disp(etaGprime)

I hope this helps! Let me know if you have any further questions.