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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

http://www.mathworks.com/products/matlab/http://www.mathworks.com/products/matlab/http://www.mathworks.com/products/matlab/