A stochastic scheme for solving definite integrals

Authors:
Saeid Abbasbandy;Mohammad Ali Fariborzi Araghi
Affiliations:
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran and Department of Mathematics, Imam Khomeini International University, Qazvin, Iran;Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran
Venue:
Applied Numerical Mathematics
Year:
2005

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Abstract

The evaluation of the definite integral I = ∫ab f(x)dx is proposed in this paper by using the stochastic arithmetic. For this purpose, the closed Newton-Cotes integration rules are considered and a theorem is proved to show the accuracy of the results. Then the CESTAC method and the stochastic arithmetic are used to validate the results and implement the numerical examples.