Performance Comparison of Numerical Integration with Percentage Error Results

Abstract

The paper presents the performance comparison of numerical integration with percentage error results for engineering applications. The numerical integration technique is a crucial role in engineering mathematics. This paper emphasizes the three different methods with different rules such as rectangular rule, trapezoidal rule and Simpson’s 1/3 rule. Numerical integration approaches are to calculate the numerical value with a definite integral range. Although some integration method cannot be solved analytically, numerical integration technique is the best way to achieve the possible solution in unknown engineering problems. In order to solve numerical integration problems in engineering applications, various techniques could be used in reality. There are three main rules in numerical integration such as Rectangular, Trapezoidal and Simpson’s rule which are widely used to solve such kinds of problems. This paper mainly focuses on identifying the method which affords more accurate result from different challenges. After that, the performance of those three rules are compared with the analytical result and checked their corresponding percentage error results. The best technique could be represented based on the observation of the minimum error values from those three analyses. The numerical values are compared to selected sets of test functions by determining the assortment of the approximation technique. MATLAB is the tool by applying the calculation of exact values, approximate values, actual errors and percentage errors. The numerical integration techniques could be utilized in telecommunication engineering and control science.

Keywords-Approximation Techniques, Numerical Intergration Method, Engineering Problem, Exact Value, Error Values.