Investigate proposed techniques to improve area calculation using Simpson and trapezoidal rules
Khalil, Ragab
The trapezoidal rule and Simpsonns rule are numerical approximation methods to be used to approximate the area under a curve. The area is divided into (n) equal pieces, called a subinterval or trapezoid. Each subinterval is approximated as a trapezoid considering the outer edge as straight line in the trapezoidal rule. In Simpsonns rule, each two subintervals approximated as a trapezoid and a parabola. This paper provides two techniques as trails to improve the area calculated using Simpsonns rule and trapezoidal rule. The first proposed technique deals with the curved part as a circular segment instead of parabola in Simpsonns rule. The second technique add or subtract a small parabola to the calculated area when using trapezoidal rule. The proposed techniques were applied on a numerical example of known area and the results show that the calculated area using the proposed techniques was improved.
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