Getting rid of fzero errors

Hey all,

I am a beginner user of MATLAB.

I have a code for solving an ODE whose solution gives the Townes soliton profile.

The code is the following:

function[]=shooting()
% Calculate R(r) in d dimensions using shooting
% Output is r_sol=[r0:dr:rf], R_sol=R(r_sol) and dR=R'(r_sol).
global R0 Dim r_inf dr_Taylor tol sigma options
Dim =2; sigma =1; r_int =15; dr=0.001; tol=1e-10;
dr_Taylor=1e-6; %when to switch from Taylor to direct formula
R0_guess = 2.2; %initial guess for R(0)
options = odeset('RelTol',tol,'AbsTol',tol);
R0 = fzero(@shoot_for_R0,R0_guess); %Find R(0) using shooting
% X is [R,R',I_R2 I_dR2 I_2sigma_2], where I_R2=int R^2 r^(d-1),
% I_dR2=int R'^2 r^(d-1), I_2sigma_2=int R^(2 sigma+2) r^(d-1)
X0 = [R0 0  0 0  0]; %X0=X(0)
[r_sol,X]=ode45(@R_profile,[0:dr:r_inf], X0, options);
R_sol = X(:,1); dR_sol=X(:,2);
plot(r_sol,R_sol,r_sol,dR_sol);legend('R','dR');xlabel('r'); shg
% Verifications - check Pohozaev identities
I_R2 = X(end, 3); I_dR2 = X(end,4); I_2sigFZERO cannot continue because user-supplied function_handle ==> shoot_for_R0 failed with the error belowma_2 = X(end,5);
Pohozaev1 = IR2-(2-sigma*(Dim-2))/2/(sigma+1)*I_2sigma_2
Pohozaev2 = I_dR2-sigma*Dim/2/(sigma+1)*I_2sigma_2
end
%
function R_inf = shoot_for_R0(R0) %R(r_inf) as function of R0
global r_inf options
X0 = [R0 0  0 0  0];
[r_sol,X]=ode45(@R_profile, [0 r_inf], X0, options);
R_inf = X(end,1);
end
%
function dX = R_profile(r,X) % Evaluate R and associated integrals
global dr_Taylor R0 Dim sigma
R = X(1); dR = X(2); dx = zeros(5,1); dX(1) = dR;
R_2sigma = abs(R)^(2*sigma);
if (r >= dr_Taylor)
    dX(2) = R-R_2sigma*R-(Dim-1)*dR/r; %R''(r)
else %Near the origin, approximate R'/r with R''(0)
    if isempty(R0)==1
        R0=0; %set arbitrary value to R0 before it is being used
    end
    ddR0 = R0*(1-abs(R0)^(2*sigma))/Dim; %R''(0)
    dX(2) = R-R_2sigma*R-(Dim-1)*ddR0; %R''(r)
end
dX(3) = r^(Dim-1)*R^2; %for I_R2
dX(4) = r^(Dim-1)*dR^2; %for I_dR2
dX(5) = r^(Dim-1)*R_2sigma*R^2; %for I_2sigma_2
end

I have to confess that I still do not understand yet much of the code but I have tried to run it and the following errors are being reported:

Error using fzero>localFirstFcnEval (line 729)
FZERO cannot continue because user-supplied function_handle ==> shoot_for_R0 failed with the error below.

 When the first argument to ode45 is a function handle, the tspan argument must have at least two elements.

Error in fzero (line 286)
    fx = localFirstFcnEval(FunFcn,FunFcnIn,x,varargin{:});

Error in townes (line 9)
R0 = fzero(@shoot_for_R0,R0_guess); %Find R(0) using shooting

Can someone please lend me a hand and tell me how to get rid of these errors?

Answer 1

[Walter Roberson]

You never assign to r_inf and it is a global variable so it is initialized to empty. You use [0 r_inf] but r_inf is empty so that is the same as just 0

The moral of the story is "Do not use global variables if you can avoid it!"

https://www.mathworks.com/help/matlab/math/parameterizing-functions.html