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% Coursework 17 Q4
% Using dx and dt as h and k are confusing
% h = dx
% k = dt
clear
dx = 0.002
% 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 = 0.1
% tfin = input('Input the time you wawnt to end the simulation (for example 0.1): ');
lines = 10
% lines = input('How many lines across the time range would you like to plot (for example 10): ');
% 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 1
% 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
% % Initial condition 2
% for i = 1:length(x)
% % u(1,i) = abs(sin(2*pi*x(i)));
% u(1,i) = sin(2*pi*x(i));
% end
% % Initial Condition 3
% for i = 0.25/dx:0.75/dx
% u(1,i) = 1;
% end
%
% Initial Condition 4
for i = 1:0.25/dx
u(1,i) = -1;
end
for i = 0.25/dx+1:0.75/dx
u(1,i) = -1+(i*dx-0.25)*4;
end
for i = 0.75/dx+1:length(x)
u(1,i) = 1;
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);
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;
j = 0
for i = 1:round(length(t)/lines):length(t)
j = j+1;
plot(x,u(i,:),'.');
legendInfo{j} = ['t = ' num2str(round(i*dt, 3))];
end
legend(legendInfo,'Location', 'southeast');
xlabel('Displacement');
ylabel('Temperature');
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