Driving Two Numerical Methods to Evaluate the Triple Integrals R(MSM),R(SMM) and Compare Between Them

  • Authors

    • Safaa M. Aljassas
    • Fouad H.A. Alsharify
    • Nada A.M. Al–Karamy
    2018-08-15
    https://doi.org/10.14419/ijet.v7i3.27.17895
  • Mid-point, dimension.

  • Abstract

    The main objective of present work is the conclusion of two new numerical methods to evaluate the triple integrals with continuous integrands and their partial derivatives are continuous too, the first method   through using Mid-point rule on the interior dimension X, Simpson's rule on the middle dimension Y and Mid-point rule on the exterior dimension Z, which denoted by the symbol MSM. The second method by using Mid-point rule on  both two dimensions of interior X and middle dimension Y and Simpson's rule on the exterior dimension Z which denoted  by SMM, where the number of divisions on the three dimensions are equals. We have concluded two theorems with their proves to find their rules and the correction terms that we found it and to improve the results we used Romberg acceleration which denoted by R(MSM),R(SMM) where we got high accuracy in the results by little sub-intervals relatively and short time.

     

  • References

    1. [1] Mohammed AH, Aljassas SM & Mohammed W, “Derivation of numerically method for evaluating triple integrals with continuous integrands and form of error (Correction terms)â€, Journal of Kerbala University, Vol.11, No.4, (2013), pp.67-76.

      [2] Dheyaa AM, “Some numerical methods for calculating single, double, and triple integrals using Matlab languageâ€, M.Sc Dissertation, University of Kufa, (2009).

      [3] Shubar AWK, “Derivation of Numerical Methods of Newton-Coates Formulas for the Calculation of Specific Triple Integrations and Improvement of Results Using Experimental Methodsâ€, M.Sc Dissertation, University of Kufa, (2014).

      [4] Ralston A , A First Course in Numerical Analysis, McGraw–Hill Book Company, (1965), pp. 87-94, 114-133, 347-348.

      [5] Eghaar BH, “Some numerical methods for calculating double and triple integralsâ€, MSc Dissertation, University of Kufa, (2010).

      [6] Ayres FJR, Schaum's Outline Series: Theory and Problems of Calculus, McGraw-Hill book-Company, (1972).

      [7] Fox L, “Romberg Integration for a Class of Singular Integrandsâ€, The Computer Journal, Vol.10, (1967), pp.87-93.

      [8] Fox L & Hayes L, “On the Definite Integration of Singular Integrandsâ€, SIAM Review, Vol.12, (1970), pp.449-457.

      [9] Jayan S & Nagaraja KV, “A general and effective numerical integration method to evaluate triple integrals using generalized Gaussian quadratureâ€, Procedia Engineering, Vol.127, (2015), pp.1041-1047.

      [10] Aljassas SM, “Evaluation of triple integrals with continuous integrands numerically by Using Method RM(RMM)â€, Journal of AL-Qadisiyah for computer science and mathematics, Vol.7, No.1, (2015), pp.1-10.

      [11] Z Yesembayeva (2018). Determination of the pedagogical conditions for forming the readiness of future primary school teachers, Opción, Año 33. 475-499

      [12] G Mussabekova, S Chakanova, A Boranbayeva, A Utebayeva, K Kazybaeva, K Alshynbaev (2018). Structural conceptual model of forming readiness for innovative activity of future teachers in general education school. Opción, Año 33. 217-240

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  • How to Cite

    M. Aljassas, S., H.A. Alsharify, F., & A.M. Al–Karamy, N. (2018). Driving Two Numerical Methods to Evaluate the Triple Integrals R(MSM),R(SMM) and Compare Between Them. International Journal of Engineering & Technology, 7(3.27), 303-309. https://doi.org/10.14419/ijet.v7i3.27.17895

    Received date: 2018-08-19

    Accepted date: 2018-08-19

    Published date: 2018-08-15