math2930_2011fa_week14&15_PS13Sol_Zehnder

# math2930_2011fa_week14&15_PS13Sol_Zehnder - 'r...

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%HW 10.8 #6 a=2; nmax=5; [R,T]=meshgrid(0:a/100:a,0:pi/100:pi); X=R.*cos(T); Y=R.*sin(T); U=0*X; for n=1:nmax; kn=4*(1-cos(n*pi))/(a^n*pi*n^3); U=U+kn*R.^n.*sin(n*T); end figure(1) h=gca; set(h, 'FontSize' ,14, 'FontWeight' , 'bold' ); surf(X,Y,U) xlabel( 'x' ) ylabel( 'y' ) zlabel( 'u(r,\theta)' ) shading interp figure(2) h=gca; set(h, 'FontSize' ,14, 'FontWeight' , 'bold' ); plot(R(1,:),U(10,:), R(1,:), U(20,:), R(1,:), U(30,:), R(1,:), U(40,:), R(1,:), U(50,:)) xlabel(

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Unformatted text preview: 'r' ) ylabel( 'u(r) for \theta=[.1,.2,.3,.4,.5]*\pi' ) figure(3) h=gca; set(h, 'FontSize' ,14, 'FontWeight' , 'bold' ); plot(T(:,1),U(:,20),T(:,1),U(:,40),T(:,1),U (:,60),T(:,1),U(:,80),T(:,1),U(:,101) ) xlabel( '\theta' ) ylabel( 'u(\theta) for r=[.2,.4,.6,.8,1.]*a' ) 1 2 3 4 0.5 1 1.5 2 2.5 u( ) for r=[.2,.4,.6,.8,1.]*a 0.5 1 1.5 2 0.5 1 1.5 2 2.5 r u(r) for =[.1,.2,.3,.4,.5]*...
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## This note was uploaded on 12/09/2011 for the course MATH 2930 at Cornell.

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math2930_2011fa_week14&15_PS13Sol_Zehnder - 'r...

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