I wanted to know how to approach this problem for a Matlab coding exercise. My inital approach was using an array and a loop to gather data before solving the differential equation but the figure was wrong. I know how to do the inputs, but as to solving the equation i am stuck. my current code is as follows:

% 1. Interactive user input h = input("Enter the value of h': "); T_infinity = input("Enter the value of T: "); sigma_prime = input("Enter the value of ': "); rod_length = input("Enter the length of the rod: "); T_start = input("Enter the temperature at the start of the rod: "); T_end = input("Enter the temperature at the end of the rod: "); num_nodes = input("Enter the number of nodes: "); % Calculate node spacing dx = rod_length / (num_nodes-1); % Initialize temperature array T = zeros(1, num_nodes); % Set boundary conditions T(1) = T_start; T(end) = T_end; % Iterate through nodes using finite difference method for i = 2:num_nodes-1 % Calculate second derivative using finite difference approximation d2T_dx2 = (T(i+1) - 2*T(i) + T(i-1)) / (dx^2); % Calculate conduction, convection, and radiation terms conduction = d2T_dx2; convection = h * (T_infinity - T(i)); radiation = sigma_prime * (T_infinity^4 - T(i)^4); % Update temperature at current node T(i) = T(i) + conduction - (convection + radiation); end % Plot temperature distribution x = linspace(0, rod_length, num_nodes); plot(x, T, 'b-'); xlabel('Distance (m)'); ylabel('Temperature (K)'); title('Temperature Distribution along the Rod'); grid on; 

A steady-state heat balance for a rod including conduction, convection and radiation can be represented as dx2d2T+h(TT)+(T4T4)=0 Where T is the surrounding temperature (T=200K). Use the finite difference method to calculate the distribution of temperature along a rod of 10m fixed to a heated plate on each end. One end of the plate is at 300K and the other end is at 400K. Use the following parameters for the solution of the equation: h=0.05m2,T=200K, and =2.7109K3 m2 1. Make a MATLAB program that interactively ask the user to input the parameters h,T,, the length of the rod, the temperature at the end and start of the rod, and the number of nodes. 2. Plot the temperature as a function of distance from one end of the rod to the other end using 100 nodes