I keep getting errors in the code when solving this question need help plz$,$ i need Matlab scripts based on the question that can solve them fullscript explanation of your codes did be great thanks, the given script from $($A$)$generate $,$ fix it and generate the other scripts needed.This is the Script NonInsulatedRod Shooting.m$\%\%-----------------------------------------------------------------$ Inputs

$\%$ NOTE: PLEASE SEARCH THE FILE FOR $\text{'}$TO DO$\text{'}$ COMMENT $-$ THESE ARE LINES THAT

$\%$ YOU NEED TO MODIFY!!

$\%$ Parameters of mathematical model

$\%$TO DO

$\%$ System of ODEs

$\%($store dependent variables in y $=[$T$,$z$],$ i$.$e$.,$ y$(1)=$ T and y$(2)=$ z$)$

$\%$ dydx $=\{$dTdx$,$dzdx$\})$

dTdx $=$ @$($x$,$y$)()$; $\%$TO DO

dzdx $=$ @$($x$,$y$)()$; $\%$TO DO

dydx $=\{$dTdx$,$dzdx$\}$;

$\%$ Parameters for numerical method

$\%$TO DO

$\%$ One$-$step algorithm for solving IVP

algorithm $=\text{'}$RK$4\text{'}$; $\%$choose 'Euler, 'Heun', $\text{'}$RK$4\text{'}$

$\%\%-----------------------------------------------------$ Plot True Solution

$\%$ True $($linear$)$ solution

$\%$TO DO

$\%$ Plot analytical solution

$\%$TO DO

$\%\%----------------------------------------------$ Nonlinear Shooting Method

$\%$ Define function handle to one$-$step IVP solver

switch algorithm

case 'Euler', oneStep $=$ @$($x$,$y$)$EulerSystem$($x$,$y$,$dydx$,$h$)$;

case 'Heun', oneStep $=$ @$($x$,$y$)$HeunSystem$($x$,$y$,$dydx$,$h$)$;

case $\text{'}$RK$4\text{'},$ oneStep $=$ @$($x$,$y$)$RK$4$System$($x$,$y$,$dydx$,$h$)$;

otherwise

error$(\text{'}$Algorithm must be $\text{'}\text{'}$Euler$\text{'}\text{'},\text{'}\text{'}$Heun$\text{'}\text{'},$ or $\text{'}\text{'}$RK$4\text{'}\text{'}\text{'})$;

end

$\%$ Solve root$-$finding problem for a

$\%$TO DO $-$ NEED ALGORITHMIC PARAMETERS

f $=$ @$($a$)$boundaryValueMismatch$($a$)$; $\%$TO DO $-$ NEED ADDITIONAL INPUTS

$\%$TO DO $-$ CALL TO ROOT FINDING FUNCTION

$\%$ Solve IVP with all intermediate values of a and plot solutions

$\%($Note this is redundant $-$ IVP has already been solved for each value of a

$\%$ during root$-$finding $-$ to keep the implementation simple, we do not worry

$\%$ about outputting solutions to the IVP during root$-$finding and re$-$solve

$\%$ the IVPs here$)-$ use a loop over a

$\%$TO DO

$\%-----------------------------------------------$

Figure $1$: Noninsulated uniform rod between two bodies of constant temperature.

Figure $1$ shows a schematic of a noninsulated uniform rod length, $L=10m,$ positioned under ambient

temperature, $T_a=20C,$ between two bodies at constant temperatures: $T_L=40C$ at the left end and $T_R=$

$200C$ at the right end. A simplified mathematical model of this system at steady state is given by the boundary

value problem $($BVP$),$

$\frac{d^{2}T}{d{x}^2}+h^{\text{'}}(T_a-T)=0,$ where $T(0)=T_L,T(L)=T_R$

where $h^{\text{'}}=0\mathrm{.}01m^{-2}$ is the heat transfer coefficient. Although the ODE in $(1)$ is linear and a linear shooting method

that interpolates between two guesses of the initial value can be used, we consider the more general nonlinear

shooting method in which root$-$finding is used to find the initial value. Such nonlinear shooting method can be used

for BVPs with linear or nonlinear ODEs.

We seek to solve the BVP in $(1)$ numerically and compare the numerical solutions to the analytical solution,

$T(x)=c_1{e}^{(\sqrt[\phantom{2}]{h^{\text{'}}})x}+c_2{e}^{(-\sqrt[\phantom{2}]{h^{\text{'}}})x}+T_a$

$c_1=T_L-T_a-c_2$

$c_2=\frac{T_R-T_L{e}^{(\sqrt[\phantom{2}]{h^{\text{'}}})L_{-}}-T_{a(1-e)(\sqrt[\phantom{2}]{h^{\text{'}}})L_{?}}}{e^{(-\sqrt[\phantom{2}]{h^{\text{'}}})L_{-}(\sqrt[\phantom{2}]{h^{\text{'}}})L}}$

Taking advantage of the fact that $(1)$ has a unique solution, we seek to solve it using the nonlinear shooting method

in which we treat the problem as an initial value problem $($IVP$)$ and iteratively adjust the initial values until the

boundary values of $(1)$ are met. To do so$,$ we convert $(1)$ to a system of first$-$order IVPs,

$\frac{dT}{dx}=z,T(0)=T_L$

$\frac{dz}{dx}=-h^{\text{'}}(T_a-T),z(0)=a$

and iterate to find the initial value, $a,$ such that the second boundary value of $(1),T(L)=T_R,$ is satisfied. The

associated problem is a root$-$finding problem in which we seek to find a such that

$T(L,a)-T_R=0$

Goals

Using the provided $($incomplete$)$ script, Script NonInsulatedRod Shooting.m$,$ write a modular Matlab code that

solves the BVP in $(1)$ via the system of IVPs in $(3)$ using the nonlinear shooting method and considering $h=1\mathrm{.}0m.$

To do so$,$ please:

$($a$)$ Complete the script.

$($b$)$ Write a function file, EulerSystem.m$,$ that performs a single step of Euler's method and can be used to solve a

system of first$-$order IVPs $($please see Fig. $3$ for a possible function header$).$

$($c$)$ Implement the main iterative loop for one$-$step methods in a separate function file, iterativelVP$-$

SolverSystem.m$.$ This function should take as input the initial values of your dependent variable $($as a vector$),$

the initial and final value of your independent variable, and a function handle, onestep, to a one$-$step method

implemented in $($b$).$ Note: This function should require very minor modifications $($if any$)$ to a similar function

written for homework $8($please see Fig. $4$ for a possible function header$).$

$($d$)$ Write a function file, boundaryValueMismatch.m$,$ that implements the function in $(4)$ for which we wish to

find the root. Since