This MATLAB function uses the trapezoidal rule to numerically integrate the function z(t) = 1/(1+100t) from t0 to tf over increasingly finer partitions (with n = 2^i subintervals) and plots the logarithm of the absolute error versus the logarithm of the step size h to demonstrate the convergence rate of the trapezoidal rule. It calculates the integral by summing the areas of trapezoids formed by function values at the partition points, and compares the result to the exact integral value of 1/101 to compute the error at each step size.

1. 11/19/14 6:32 AM C:Usersphui3Trapezoidal.m 1 of 1
function Trapezoidal(t0,tf)
for i = 1:5
n = 2^(i-1);
middle = 0;
dt = (tf-t0)/n;
t = t0:dt:tf;
y(1) = 1;
if n >= 2
for j = (t0+dt):dt:(tf-dt)
middle = middle + 2*z(j);
end
end
trapezoid = (dt/2)*(z(t0) + middle + z(tf));
n
trapezoid
h(i) = dt;
e(i) = abs((1/101) - trapezoid);
end
plot(log(h), log(e));
xlabel('log h');
ylabel('log absolute error');
end
function z = z(t)
z = (1/(1+100*(t)));
end