Solution6

Solution6 - ChE132B HW#6 Solutions(60pt Problem1(20pt...

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Unformatted text preview: ChE132B HW#6 Solutions (60pt) Problem1 (20pt) function [ginf,x,y]=hw61(h0) % define a function to use the shooting method, 5pt n=20; xi=0; xf=10; fi=0; gi=0; hi=h0; yi=[fi;gi;hi]; [email protected](x,y) [y(2);y(3);-0.5*y(1)*y(3)]; [x,y]=RungeKuttaM(func,xi,yi,xf,n); ginf = y(2,n+1)-1; function [x,y] = RungeKuttaM(func,xi,yi,xf,n) % 5pt , the multidimensional Runge-Kutta method x=zeros(1,n+1); s=length(yi); y=zeros(s,n+1); p=ones(s,1); x(1)=xi; y(:,1)=yi; h=(xf-xi)/n; for i=1:n x(i+1) = x(i)+h; k1 = feval(func,x(i),y(:,i)); k2 = feval(func,x(i)+0.5*h,y(:,i)+0.5*k1*h.*p); k3 = feval(func,x(i)+0.5*h,y(:,i)+0.5*k2*h.*p); k4 = feval(func,x(i)+h,y(:,i)+k3*h.*p); y(:,i+1) = y(:,i)+(k1+2.*(k2+k3)+k4)*h/6.*p; end % 5pt , the Blasius frictional drag coefficient, Cd. >> Cd=fzero(@hw61, [0.1,1],optimset( 'TolX' ,1e-4)) Cd = 0.3321 % 5pt , plot f, f’, f’’ vs. z. [ginf,x,y]=hw61(Cd); subplot(3,1,1) plot(x,y(1,:)) xlabel( 'z' ) ylabel( 'f(z)' ) subplot(3,1,2) plot(x,y(2,:)) xlabel( 'z' ) ylabel( 'df/dz' ) subplot(3,1,3) plot(x,y(3,:)) xlabel( 'z' ) ylabel( 'd2f/d2z' ) Problem2 (20pt) function [x,y,dy,iter]=hw62(N) % 3pt , Chebyshev differentiation [D,x]= chebD(N); D2 = D^2; x=5*x; % rescale x D2(1,:) = zeros(1,N+1); D2(1,1) = 1.; % for right boundary condition D2(N+1,:) = zeros(1,N+1); D2(N+1,N+1) = 1 ; % for left boundary condition err=1; iter=0;...
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Solution6 - ChE132B HW#6 Solutions(60pt Problem1(20pt...

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