mae200b_hw3
TRANSCRIPT
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FIGURES
Figure 1- Problem 1
Figure 2 Problem 2
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Figure 3 Problem 3
MATLAB CODE
Contents
PROBLEM 1
PROBLEM 2
PROBLEM 3
%MAE 200B HW3
%Laura Novoa
PROBLEM 1
clc
clear all
close all
k = 0.1;
a = 1;
N = 50;
%First 50 zeros of J0(x)
z0=besselzero(0, 50, 1);
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syms x
u_inf = 1/2;
f = sin(pi*abs(x)/a) - u_inf;
%Fourier Bessel coefficients
forj=1:N
B(j)=double(int(f*x*besselj(0, z0(j)*x/a), 0, a));
B(j)=2*B(j)/(a* besselj(1, z0(j)))^2;
end
%X ,T mesh for plotting
[X,T] = meshgrid(0:0.01*a:a,0:.2:5);
%Reconstruction of the function
fsim=0;
forj=1:N
fsim = fsim + B(j)*besselj(0, z0(j)*X/a).*exp(-k.*(z0(j)/a).^2.*T);
end
U = u_inf + fsim;
mesh(X,T,U)
xlabel('r')
ylabel('t')
zlabel('u')
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PROBLEM 2
clear all
clc
close all
k = 0.1;L = 1;
N = 30;
syms x
f = 4.*abs(x)/L - 4.*(x/L).^2;
%Fourier cosine coefficients
forj=1:N
B(j)= double(int(f*cos((j)*pi*x/L), -L, L))/L;
end
%X,T mesh for plotting
[X,T] = meshgrid(0:0.01*L:L,0:.2:5);
%Reconstruction of the function
fsim=0;
forj=1:N
fsim = fsim + B(j)*cos((j)*pi*X/L).*exp(-k*((j)*pi/L). 2.*T);
end
B_o = int(f,-L,L)/L; % SS solution
U = B_o/2 + fsim; % Accounts for the SS solution, i.e., if n=0
mesh(X,T,U)
xlabel('x')
ylabel('t')
zlabel('u')
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PROBLEM 3
clc
clear all
close all
k = 0.1;
a = 1;
N = 10;
%First 50 zeros of J0(x)
z0=besselzero(0, 50, 1);
z1=besselzero(1, 50, 1);
z1_0 = [0; z1]; % concatenating 0 as z10
syms x
f = 4.*abs(x)/a - 4.*(x/a).^2;
%Fourier Bessel coefficients
forj=1:N
B(j)=double(int(f*x*besselj(0, z1_0(j).*x/a), 0, a));
B(j)=2*B(j)/(a.*besselj(0, z1_0(j))).^2;
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end
%X,T - mesh for plotting
[X,T] = meshgrid(0:0.01*a:a,0:.2:5);
%Reconstruction of the function
fsim=0;
forj=1:N
fsim = fsim + B(j)*besselj(0,z1_0(j)*X/a).*exp(-k.*(z1_0(j)/a).^2.*T);
end
%u_inf = besselj(0,0);
U = fsim;
mesh(X,T,U)
xlabel('r')
ylabel('t')
zlabel('u')
Published with MATLAB R2015a
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