Applied Mathematics, 2015, 6, 958-966 Published Online June 2015 in SciRes. http://www.scirp.org/journal/am http://dx.doi.org/10.4236/am.2015.66088 How to cite this paper: Hashemiparast, S.M., Ghondaghsaz, D.A. and Maghasedi, M. (2015) Numerical Approximation of Quantum-Integrals Using the Appropriate Nodes and Weights. Applied Mathematics, 6, 958-966. http://dx.doi.org/10.4236/am.2015.66088 Numerical Approximation of Quantum-Integrals Using the Appropriate Nodes and Weights S. M. Hashemiparast 1,2 , D. A. Ghondaghsaz 2 , M. Maghasedi 2 1 School of Mathematics, KNT University of Technology, Tehran, Iran 2 Department of Mathematics, College of Basic Sciences, Karaj branch Islamic Azad University, Alborz, Iran Email: hashemiparast@kntu.ac.ir Received 18 April 2015; accepted 30 May 2015; published 2 June 2015 Copyright © 2015 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract In this paper, we present a procedure for the numerical q-calculation of the q-integrals based on appropriate nodes and weights which are determined such that the error of q-integration is mini- mized; a system of linear and nonlinear set of equations respectively are prepared to obtain the nodes and weights simultaneously; the error of q-integration is considered to be minimized under this condition; finally some application and numerical examples are given for comparison with the exact solution. At the end, the related tables of approximations are presented. Keywords q-Calculation, Numerical Approximation, q-Integration, q-Derivative 1. Introduction Recently, much attention has been paid on q-calculus, especially on q-fractional calculus which finally most of them have changed to q-integral not easy and even possible to be solved analytically [1]. Although some series expansions have been developed for quantum integrals [2] and quantum differential equations and quantum dif- ference equations [3]-[6] or q-fractional calculus [6] [7], but because of small fractional power in the series ex- pansion, one will expect a high degree of error in the truncated series [7]-[9]. The nominal numerical methods for approximating integrals do not seem to be appropriate for q-integrals. We could find less works for develop- ing numerical procedures for accurate numerical solutions [9]-[14]. In this paper, we present a procedure for the numerical q-calculation of the q-integrals based on appropriate nodes and weights which are determined such that the error of q-integration is minimized. This study is organized such that in Section 2 we introduce the basic