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Math. Comput. Appl. 2002, 7(1), 83-91; doi:10.3390/mca7010083

Numerical Solution of Improper Integrals with Valid Implementation

1
Department of Mathematics, Imam Khomeini International University, Qazvin, P.O. Box 288, Iran
2
Department of Mathematics, Islamic Azad University, Science and Research Branch, Tehran, Iran
*
Authors to whom correspondence should be addressed.
Published: 1 April 2002
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Abstract

In this paper, two theorems are explained which are used in order to find the improper integral I = \({\int_a^\infty}\)f(x)dx numerically. It has been proved in [4], one can use the Trapezoidal and Simpson rules to find the definite integral Im = \({\int_a^\infty}\)f(x)dx numerically using the CESTAC (Control et Estimation Stochastique des Arrondis de Calculs ) method which is based on the stochastic arithmetic, [5-8,12]. These theorems are developed on the improper integrals. Then, the CESTAC method and stochastic arithmetic are used to validate the results and implement the numerical examples. By using this method, one can find the optimal integer number m ≥ 1 such that I ~ Im. In the last section two examples are solved. The programs have been provided with Fortran 90.
Keywords: Stochastic Arithmetic; CESTAC method; Trapezoidal rule; Simpson rule; Improper Integrals Stochastic Arithmetic; CESTAC method; Trapezoidal rule; Simpson rule; Improper Integrals
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Abbasbandy, S.; Fariborzi Araghi, M.A. Numerical Solution of Improper Integrals with Valid Implementation. Math. Comput. Appl. 2002, 7, 83-91.

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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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