working solution for ex4

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+% 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; 
+    u(m+1,length(x)) = 0;
+    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