hw13_solutions

hw13_solutions - b = [pi/9, sqrt(3)/2 sqrt(3)/2 -pi/9]; N =...

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Section 2.4
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Section2.5
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Problem 3 (2.5 11a) %% section 2.5 11a clear close all clc h = 2.^(-1:-1:-7); N = 1./h; for k = 1:7 I = 0.2*atan(5); %%%%%%%% left-endpoint rectangular rule %%%%%%%%% x1 = 0:h(k):1-h(k); fx1 = 1./(1 + 25*x1.^2); T1(k) = h(k)*sum(fx1); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%% trapezoid rule %%%%%%%%%%%%%%% x2 = 0:h(k):1; fx2 = 1./(1 + 25*x2.^2); T2(k) = h(k)/2*(fx2(1) + 2*sum(fx2(2:end-1)) + fx2(end)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% end err1 = T1 - I; err2 = T2 - I; figure plot(log(h),log(abs(err1))); hold on plot(log(h),log(abs(err2)), 'r' ); legend( 'left-endpoint' , 'trapeziod' ) xlabel( 'h' ) ylabel( 'error' ) grid on -5 -4 -3 -2 -1 0 -15 -10 -5 0 h error left-endpoint trapeziod
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Section 2.6 2. The answer from matlab code is below x = 0.008494710254722 0.157543504689989 0.227356674769762 -0.200944799984597 The code is below %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% section 2.6 2 clear clc close all l = [0 1 1 2]; d = [4 4 4 4]; u = [2 1 1 0];
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Unformatted text preview: b = [pi/9, sqrt(3)/2 sqrt(3)/2 -pi/9]; N = length(d); x = zeros(N,1); for k = 2:N d(k) = d(k) - u(k-1)*l(k)/d(k-1); b(k) = b(k) - b(k-1)*l(k)/d(k-1); end x(N) = b(N)/d(N); for k = N-1:-1:1 x(k) = (b(k) - u(k)*x(k+1))/d(k); end display(x) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Section 2.7 3 The answer from matlab is below x = 0.018336695058824 0.035006775977942 0.048317587771715 0.056523986874421 0.057801073272040 0.050215676439535 0.031696149551397 The code is here %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 %% section 2.7 3 clear clc close all M = 8; N = M-1; h = 1/M; l = -1*ones(N,1); l(1) = 0; d = ones(N,1)*(2+h^2); u = -1*ones(N,1); u(end) = 0; b = (h:h:N*h)*h^2; x = zeros(N,1); for k = 2:N d(k) = d(k) - u(k-1)*l(k)/d(k-1); b(k) = b(k) - b(k-1)*l(k)/d(k-1); end x(N) = b(N)/d(N); for k = N-1:-1:1 x(k) = (b(k) - u(k)*x(k+1))/d(k); end display(x) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Created by Jianjian Gao 2010/10/12...
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hw13_solutions - b = [pi/9, sqrt(3)/2 sqrt(3)/2 -pi/9]; N =...

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