I keep getting the following error code in my MATLAB code, and I can not figure out how to fix it$.$ Below is the error code I keep receiving, followed by my MATLAB code. What do I need to change in my code to correct the problem?

Error using fzero $($line $308)$

Initial function value must be finite and real.

Error in main $($line $18)$

z$0=$ fzero$($@$($z$0)$ shooting$\_$method$($x$,$ z$0,$ L$,$ sigma$\_$prime, T$\_$inf, T$0,$ TL$),$ z$0\_$guess$)$;

MATLAB CODE:

function main$()$

L $=10$; $\%$ Length of the rod $($m$)$

N $=100$; $\%$ Number of spatial grid points

$\%$ Constants

sigma$\_$prime $=2\mathrm{.}7$e$-9$; $\%$ K$^-3$ m$^-2$

T$\_$inf $=298$; $\%$ K

$\%$ Boundary conditions

T$0=400$; $\%$ K at x$=0$

TL $=600$; $\%$ K at x$=$L

$\%$ Spatial grid

x $=$ linspace$(0,$ L$,$ N$+2)$; $\%$ Including boundary points

$\%$ Shooting Method

z$0\_$guess $=0\mathrm{.}01$; $\%$ Initial guess for z$(0)$

z$0=$ fzero$($@$($z$0)$ shooting$\_$method$($x$,$ z$0,$ L$,$ sigma$\_$prime, T$\_$inf, T$0,$ TL$),$ z$0\_$guess$)$;

$[$~$,$ T$\_$shooting$]=$ shooting$\_$method$($x$,$ z$0,$ L$,$ sigma$\_$prime, T$\_$inf, T$0,$ TL$)$;

$\%$ Finite Difference Method

T$\_$fd $=$ finite$\_$difference$\_$method$($L$,$ N$,$ sigma$\_$prime, T$\_$inf, T$0,$ TL$)$;

$\%$ Plotting

figure;

plot$($x$,$ T$\_$shooting, $\text{'}$b$-\text{'},$ 'LineWidth', $2)$;

hold on;

plot$($x$,$ T$\_$fd$,\text{'}$r$--\text{'},$ 'LineWidth', $2)$;

hold off;

xlabel$(\text{'}$x $($m$)\text{'})$;

ylabel$(\text{'}$Temperature $($K$)\text{'})$;

title$(\text{'}$Temperature Distribution in a Rod'$)$;

legend$(\text{'}$Shooting Method', 'Finite Difference Method'$)$;

grid on;

end

function $[$residual$,$ T$]=$ shooting$\_$method$($x$,$ z$0,$ L$,$ sigma$\_$prime, T$\_$inf, T$0,$ TL$)$

$\%$ Shooting Method Solver

$\%$ Number of spatial grid points

N $=$ length$($x$)-2$;

$\%$ Spatial step size

dx $=$ L $/($N $+1)$;

$\%$ Initialize y and z vectors

y $=$ zeros$($N$+2,1)$;

z $=$ zeros$($N$+2,1)$;

$\%$ Set initial conditions

y$(1)=$ T$0$;

z$(1)=$ z$0$;

$\%$ Numerical integration using Euler's method

for i $=1$:N$+1$

z$($i$+1)=$ z$($i$)+$ dx $*(-$sigma$\_$prime $*($T$\_$inf $-$ y$($i$)^4))$;

y$($i$+1)=$ y$($i$)+$ dx $*$ z$($i$+1)$;

end

$\%$ Calculate the residual at the right boundary $($x$=$L$)$

residual $=$ y$($end$)-$ TL;

T $=$ y;

end

function T $=$ finite$\_$difference$\_$method$($L$,$ N$,$ sigma$\_$prime, T$\_$inf, T$0,$ TL$)$

$\%$ Finite Difference Method Solver

$\%$ Spatial grid

x $=$ linspace$(0,$ L$,$ N$+2)$; $\%$ Including boundary points

$\%$ Spatial step size

dx $=$ L $/($N $+1)$;

$\%$ Coefficient matrix for finite difference equation

A $=$ diag$(-2*$ones$($N$,1))+$ diag$($ones$($N$-1,1),1)+$ diag$($ones$($N$-1,1),-1)$;

A $=$ A $/$ dx$^2$;

$\%$ Right$-$hand side vector

b $=$ sigma$\_$prime $*($T$\_$inf $-$ T$0^4)*$ ones$($N$,1)$;

b$(1)=$ b$(1)-$ T$0/$dx$^2$;

b$($end$)=$ b$($end$)-$ TL$/$dx$^2$;

$\%$ Solve the system of equations

T$\_$interior $=$ A$\backslash$b;

$\%$ Concatenate the boundary conditions to get the final temperature profile

T $=[$T$0$; T$\_$interior; TL$]$;

end