% Coursework 17 Q4
% Using dx and dt as h and k are confusing
% h = dx
% k = dt

dx = input('Input position step (for example 0.01): '); % play about with this to get resolution

% Calulate maximum dt to maintain stability, based on the tailor expansion.
dt = dx^2/2;

tfin = input('Input the time you wawnt to end the simulation (for example 0.1): ');

lines = input('How many lines across the time range would you like to plot (for example 10): ');

% v = dx/(dt^2); %redundant

% Create x and t for plotting in the array
x = 0:dx:1;
t = 1:dt:tfin+1;

% Initialization of temperature matrix advancing in time (rows) and space (columns)
u = zeros(length(t),length(x)); 
u(1,:) = 0;
u(1,length(x)) = 0;

% Initial condition
for i = 1:length(x)
    if x(i) <= 0.5
        u(1,i) = 2*x(i);;
    else
        u(1,i) = 2*(1-x(i)); 
    end
end
        

for m = 1:length(t)
    % Set boundaries
    u(m+1,1) = 0.5 * m /length(t); 
    u(m+1,length(x)) = 0.5 * m /length(t); 
    for j = 2:(length(x)-1)
        % multiply out (1-2v) and factorise out v
        u(m+1,j) = u(m,j) + ((dt/(dx^2))*(u(m,j+1) - 2*u(m,j) + u(m,j-1))); 
    end
end

figure;
hold on;
for i = 1:round(length(t)/lines):length(t)
    plot(x,u(i,:),'.');
end