Definição intervalar do método de integração dos trapézios

Abstract

When working with numerical calculation in a computacional system, we operate on floating-point numbers. This way, the result is only an aproximation and errors generatedbyarredondationsortruncationscanleadtoincorrectresults. One of the alternatives to bypass the errors caused by the machine is the utilization of intervals arithmetic which makes possible to obtain intervals results with greater accuracy and with a lower contained error. Numerical methods look for develop algorithms using a finite sequence of basic arithmetic operations. When it is not possible to find the primitive of a function in its analitic form, we can not use other method than the numerical method. Being the numerical integration obtained through aproximation the result is affected by errors. In the literature there are interval integration methods, such as the Moore Integral, Bedregal Integral, Rall Integral, and Interval Simpson Method, but still the interval form of Trapezoidal method is not defined. In this context, the present work has as objective to define the interval form of the Trapezoidal method, using the interval extension method, to, posteriorly, implementate the method in a programation environment that supports the interval type. In order to verify the results obtained, a numerical analysis was performed by calculating the diameter of the interval, and the relative and absolute errors. In addition, a comparison was made with the Simpson interval method. When using the interval trapezoidal method, it was possible to obtain interval results with acceptabIe errors and to mantain a lower processing time than that obtained when using the interval Simpson method.