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