Comparison between trapezoidal rule and Simpsons rule
1 Answer
Sr.no Trapezoidal rule simpson's rule
1 Area of irregular piece of land obtain by trapezoidal rule is not accurate like Simpson’s rule Area of irregular piece of land obtain by Simpson’s rule the
2 In this method the boundary between the end of ordinate and straight line. Thus the area enclosed between the baseline and the irregular boundary is dividing into series of trapezoids. In this method required baseline even number of division of the area i.e. the total number of ordinate must be odd. If there is a then the the of an last division must be determine separately.
3 $ A = {\frac{h}{2}}[{({y_1 + y_2})+({y_2 + y_3})+....+({y_n + y_{n+1})}}]\\ [{({y_1 + y_2})+({y_2 + y_3})+....+({y_n + y_{n+1})}}]$ = sum of all parallel ordinate or offset ; n=1,2,3,4 ; h = width of strip $ A = {\frac{h}{3}}[{({y_1 + y_n})+4({y_2 + y_4 + ...}) + 2({y_3 + y_5 + ...})}] \\ ({y_1 + y_n})$ =sum of extreme ordinate ; $({y_2 + y_4 + ...})$ =sum of even ordinate ; $ ({y_3 + y_5 + ...})$ =sum of odd ordinate ; h=width of strip
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