Question

How would you code this on matlab?

Wirite a code to find an approximation for the composite trapezoidal rule. dr witiferent mumber of sabintervals using Use the following number of subintervals namely, n 10,n 20,n-40 andn 100 and calculate the global errors in each case.

Answer 1

n = input('number of intervals:');
ar = zeros(1,n+1);
b = input('upper limit:');
a = input('lower limit:');
f = @(x) sin(x.^3)./(x + 2);
h = (b - a)/n;
ar(1) = a;
% for loop to create array of points
for i=1:n
ar(i+1) = ar(1) + h*i;
end
% following is the composite trapezoidal rule
T = @(h, ar) h./2.*(f(ar(1)) + f(ar(n+1))) + h.*sum(f(ar(2:n)));

% evaluating result
answer = T(h, ar);
disp('the answer is');
disp(answer);
disp('the global error is');
q = integral(f, 0, 2);
disp(abs((answer - q)));

ANSWERS:

>> cheg_composite_rule
number of intervals:10
upper limit:2
lower limit:0
the answer is
0.1546

the global error is
0.0015

>> cheg_composite_rule
number of intervals:20
upper limit:2
lower limit:0
the answer is
0.1557

the global error is
4.1113e-04

>> cheg_composite_rule
number of intervals:40
upper limit:2
lower limit:0
the answer is
0.1560

the global error is
1.0362e-04

>> cheg_composite_rule
number of intervals:10
upper limit:2
lower limit:0
the answer is
0.1546

the global error is
0.0015