Can someone help me create a vector R for my MATLAB code. See the question below code. n = 4; %sub intervals in the x dimension dt = 0.1; %delta t tsteps = 30; alpha = 0.5; dx = 1; %delta x uL = @(t) t; %left boundary uR = @(t) t+1; %right boundary u0 = @(x) x.^2; %initial condition gamma = alpha*dt/(2*(dx^2)); %change beta to reflect average A = zeros(n+1,n+1); x = linspace(0,1,n+1); %start, finish, number of points t = linspace(0,tsteps*dt,tsteps+1); %Initial conditions %create a tridiagonal matrix for A A(1,:) = [1+2*gamma,-gamma,0,0,0]; A(2,:) = [-gamma,1+2&gamma,-gamma,0,0]; A(3,:) = [0,-gamma,1+2*gamma,-gamma,0]; A(4,:) = [0,0,-gamma,1+2*gamma,-gamma]; A(m-1,:) = [0,0,0,-gamma,1+2*gamma]; % % create a matrix for R(j,n) %R(j,n) = gamma*u(j-1,n) + (1-2*gamma)*u(j,n) + gamma*u(j+1,n) % R = zeros(n+1,1);%R matrix from notes % R(1) = R(1,n) + gamma*uL(t+1); % R(2) = R(2,n); % R(3) = R(3,n); % R(4) = R(4,n); % R(m-1) = R(m-1,n) + gamma*uR(t+1); %what the hell is m?? Confused me when he kept switching m and n %call tridfun %a = [1+2*gamma,1+2*gamma,1+2*gamma,1+2*gamma,1+2*gamma] %b = [-gamma,gamma,gamma,gamma,gamma,] %c = [-gamma,gamma,gamma,gamma,gamma,] %k = [R(1,n),R(2,n),R(3,n),R(4,n),R(m-1,n)] %u=tridfun(a,b,c,k) 

1) Write Matlab code to implement the Crank-Nicolson method to solve the one-dimensional heat equation u(t, 0) = a(t) u(t, 1) = (t) and initial condition u(0, g( Here c is a positive constant. Note that the boundary condition functions a and are not constant: they are functions of t. Employ the proper tridiagonal solving strategy. Use Matlab's contourf and colorbar commands to illustrate your results. 2) Repeat exercise 1) above, but this time use the boundary conditions a(t, 0) = a(t) u t, 1(t) Use the "fictitious node" technique for the Neumann boundary condition