% Matlab program to calculate transient heat flow in a heated dike over time using fourier transforms (fft)
% Notes: find how to set "double precision" to all values
clear all;
figure(1);
%%%%%% PARAMETERS %%%%%%
% (Matlab already has "pi" set to 3.1416, try it!)	
n=32   	    % choose a number which is a exponent of 2
kapp = 
d = 
start_temp = 
time =      % you will change this value for each time interval

%%%%%% SET STARTING TEMPERATURE PROFILE (from 1 to n)%%%%%%
%(Hint: you may need to include an "antidike" to keep your boundary conditions) %

for j = 1,n
   T = 
end 

plot(T,n,'^')
hold on
plot(T,n)
xlabel('distance (units)')
ylabel('Temperture (units)')
Title('Heated Dike, Lab #3, #...days')

%%%%%% TAKE FAST FOURIER TRANSFORM (FFT) of your Temp function %%%%
% (You are now working in frequency (or in this case - wave number) space
% (This will output a coefficient in alternating sine,cos for each point) 

dfft(T,n)

%%%%% GET FOURIER COEFFICIENTS (Bo, An, Bn) %%%%%%

COEFF(1) = T(1)/2
COEFF(2) = T(2)/2
for j = 3:2:n		% increment from 3 to n by 2's
   COEFF(j) = T(j)
   COEFF(j+1) = T(j+1)
end

%%%%%%  SOLVE FOR TEMPERATURE CHANGE using solution to heatflow eqn %%%%%

for j = 3:2:n
   NEWT = T(j).*exp(put relevant stuff here)
   NEWT = T(j+1).*exp(stuff here)
end

NEWT = T(2)*exp(stuff here)

%%%%%% Recover TEMP function by taking INVERSE FOURIER TRANSFORM %%%%%
% (This will bring you back to Temperature and time space) %
% and plot your final conductive temperture profile! %

ift(NEWT,n)

plot(n,NEWT,'or')
plot(n,NEWT,'r')
hold off