Answer Happy

i) Show that the error of trapezoidal and mid-ordinate rule is
proportional to 𝑑2 ( 𝑑=𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙) and error of
Simpson’s rule is proportional to 𝑑4.
ii) Show that doubling the number of intervals will reduce the
error by a factor of 0.25(error multiplier) for the trapezoidal and
mid-ordinate rule.
iii) Find the error multiplier for Simpson’s rule.
iv) Find the differences between successive approximates for
each of the 3 methods.
v) Show that ratio of differences between successive estimates
is equal to the error multiplier for each method.
1 » S = 6x5 dx 0