NSSC/Exercise_03/NSSC_3.m

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%% exercise number 2
%problem characteristics
U=0.7;%convection velocity
delta_x=0.01; %space discretization
L=1; %max length of our domain
T=1; %max time considered
N=L/delta_x; %number of intervals in space
K=100; %number of intervals in time
%two initial conditions
square_pulse=@(x) heaviside(x-0.1) - heaviside(x- 0.3);
gauss_signal=@(x) exp(-10*(4*x - 1).^2);
[x,t,c] = UW_scheme(L,N,T,K,U,square_pulse);
ex_sol=@(x,t) square_pulse(x-U*t);
f1=figure(1);
for ii=1:K+1
clf(f1)
hold on
plot(x,c(:,ii)','-bo');
plot(x,ex_sol(x,t(ii)));
hold off
legend("aproximated solution","exact solution")
xlim([0 L])
ylim([0 1.1])
pause(0.02);
end
[x,t,c] = UW_scheme(L,N,T,K,U,gauss_signal);
ex_sol=@(x,t) gauss_signal(x-U*t);
f2=figure(2);
for ii=1:K+1
clf(f2)
hold on
plot(x,c(:,ii)','-bo');
plot(x,ex_sol(x,t(ii)));
legend("aproximated solution","exact solution")
xlim([0 L])
ylim([0 1.1])
pause(0.02);
end