Modified Trapezoidal Rule Based Different Averages for Numerical Integration

Abstract

In this paper, A Modified Trapezoidal Rule is presented for the evaluation of numerical integration; the proposed method appears to be efficient modification of trapezoidal rule which is the composition of arithmetic mean of subintervals while the proposed method uses arithmetic mean and Heronian mean at the subintervals. The accuracy of this rule is higher than the original trapezoidal rule .the comparison between the modified trapezoidal rule and original trapezoidal rule is made by using numerical experiments on the basis of local truncation Error.

Keywords: Modified trapezoidal rule, Arithmetic mean, Heronian mean, Numerical examples, Accuracy, Numerical Integration.