Topic 13.2: Composite-Trapezoidal Rule (Matlab)

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Finding approximate the integral using the composite trapezoidal rule, of a function f(x) = cos(x):

format long
eps_step = 1e-5;
N = 20;
a = 0;
b = 10;
h = b - a;

ctrap = 0.5*(cos(a) + cos(b))*h;

for i=1:N
    h = h/2;
    ctrapn = 0.5*(cos(a) + 2*sum( cos( (a + h):h:(b - h) ) ) + cos(b))*h;

    if abs( ctrap - ctrapn ) < eps_step 
       break;
    elseif i == N
       error( 'The composite trapezoidal rule did not converge' );
    end

    ctrap = ctrapn;
end

ctrapn

What happens if you remove the conditional statement and simply approximate the integral with larger and larger numbers of sub-intervals? (Try N = 100;)

Copyright ©2005 by Douglas Wilhelm Harder. All rights reserved.