Evaluation Of Double Intergral Using Simpson's Rule

Evaluation of Double Intergral Using Simpson's rule :

This is the another method of evaluating double integral.

We consider the evaluation of the double integral,

over a rectangle                  x = a, x = b, y = c, y = d

figure  : 1.1 region of integral

To apply the Simpson’s rule, let h = (b – a)/2 and k = (d – c)/2.

Evaluating the inner integral by Simpson’s rule, we obtain

..................1.1

Where

Evaluating the integral again by Simpson’s rule, we obtain

...................1.2

The weights (coefficients of the ordinates f ) in the Simpson’s rule are given in the computational molecule (Fig.1.2 ) below

figure : 1.3 weights in simpson's rule