MATLAB: I’m facing some problems in utilizing the plot result provided by the program (given below) for further calculations.

numerical integrationplotvariable

The plot provided by the program is required for the evaluation of the E(S) along with the variable used in the code. The code is as follows;
   function TestSmooth(lambda,a,b,AbsTol,RelTol,c)
   behavior =1;
   if nargin < 4 || isempty(AbsTol)
    AbsTol = 1e-6;
    end
    if nargin < 5 || isempty(RelTol)
    RelTol = 1e-3;
    end
    if nargin < 6 || isempty(c)
    c = -1;
    end
    % Compute and plot the solution:
    [soln,errest,cond] = Fie(lambda,a,b,behavior,@kernel,@RHS,AbsTol,RelTol);
    t = soln.s; sol = soln.x; 
    nfinal = length(t) - 1;
    % Interpolate the solution for assessing the error and if necessary,
    % use to get a smooth graph.
    tint = linspace(a,b,150);
    xint = ntrpFie(soln,tint);
        if nfinal < 150
    plot(tint,xint) 
    h = findobj(gca,'Type','line');
    x1=get(h,'Xdata');
    y1=get(h,'Ydata');
    J=@(S)bessel(0,S./aa.*aa.*x1.^2);
    J1=@(S)(x1.^2).*y1.*J(S);
    int=trapz(x1,J1(S)); 
    E=((pi.*aa.*aa.*1e-6)./(210e9)).*int;
    disp (E);
        else
    plot(t,sol)
        end
    %====Nested functions=======================================================
    function kst = kernel(s,t)
     nn=8;
    l=1*17.6e-6; % microstructural characteristic length
    aa=17.6e-6;% crack length
    h=10*aa;% half-height of the plate
    a_est=@(S)1+(1./((S./aa).^2.*(l.^2)));%a* exp(-2.*h.*sqrt(((S./aa)).^2+(1./l.^2))
    b_est1=@(S)exp(-(S./aa).*h)-exp(h.*sqrt(((S./aa)).^2+(1./l.^2)));
    b_est2=@(S)-exp(-h.*sqrt(((S./aa)).^2+(1./l.^2)))+exp(h.*sqrt(((S./aa)).^2+(1./l.^2)));
    b_est=@(S)b_est1(S)./b_est2(S);%b*
    P1=@(S)(((1+exp(-2.*(S./aa).*h))./a_est(S)))
    P2=@(S)exp(-2.*h.*sqrt((S./aa).^2+(1./l.^2)));
    P3=@(S)1./(1+(exp(-2.*(S./aa).*h)).*P2(S));
    P=@(S)P3(S).*((1+exp(-2.*(S./aa).*h))-P1(S));
    F3=@(S)(1-exp(-2.*(S./aa).*h))./(P(S).*(1+exp(-2.*(S./aa).*h)));
    f21=@(S)S.*(F3(S)-1).*besselj(0,S.*s.^2).*besselj(0,S.*t.^2);
    f2=@(S)-2.*t.*s.*t.*f21(S);
    kst=galag(f2,nn);
    end % kernel
    function ts = true_soln(t)
    ts = 0;
    end % true_soln
    function rs = RHS(s)
    rs=s;
    end % RHS
    end
It showed me the following error
Undefined function or variable 'S'.
Error in TestSmooth (line 48) int=trapz(x1,J1(S));
Thanks in advance.

Best Answer

Change
      int=trapz(x1,J1(S));
to
      int=trapz(x1,J1(x1));
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