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Approximate Solution of Real Definite Integrals in Adaptive Routine


  • Department of Mathematics, School of Applied Sciences, KIIT University, Bhubaneswar – 751024, Odisha, India


A mixed quadrature rule of higher precision has been formulated by taking two constituent rules each of lower degree of precision. Mixed quadrature rule in adaptive environment is used for evaluation of real definite integrals over a circle or triangle which is best fit to the Fracture Mechanics. Mixed quadrature rules have been applied in various fields of Science and Technology. Objectives: Mixed quadrature rule has become a milestone in the field of Science and Technology. Methods/Statistical Analysis: A mixed quadrature rule of degree of precision nine has been formed by taking two constituent rules each of degree of precision seven. Findings: The mixed quadrature rule has been tested in adaptive routine and it has found to be more effective than that of Clenshaw-curtis seven-point rule. Application: Mixed quadrature rule in adaptive environment is used for evaluation of real definite integral over a circle or triangle which is best fit to the fracture mechanics.


Adaptive Quadrature Method, Degree of Precision, Maclaurin’s Series, Mixed Quadrature Rule M.SC 2010: 65D30,65D32.

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  • Bradie B. A friendly introduction to numerical analysis, Pearson; 2007.
  • Davis JP, Rabinowitz P. Methods of numerical integration, 2nd Ed., Academic Press Inc., San Diego; 1984.
  • Walter G, Walter G, Adaptive quadrature – Revisited. BIT Numerical Mathematics. 2000; 40(1):84–109.
  • Oliver J. A doubly adaptive Clenshaw-Curtis quadrature method. Computing centre, University of Essex, Wivenhoe Park, Colchester, Essex. 1971; 15(2):141–7.
  • Das RN, Pradhan G. A mixed quadrature rule for approximate evaluation of real definite integral. International Journal of Mathematical Education in Science and Technology. 1996; 27(2):279–83.
  • Jena SR, Dash P. Approximation of real definite integrals via hybrid quadrature domain. International Journal of Science Engineering Technology and Research. 2014; 3(12):3188–91.
  • Jena SR, Dash RB. Study of approximate value of real definite integral by mixed quadrature rule obtained from Richardson extrapolation. International Journal of Computer Science and Mathematics. 2011; 3(1):47–53.
  • Ma RJ, Wandzura SV. Generalised Gaussian quadrature rules for systems for systems of arbitrary functions. SIAM Journal of Numerical Analysis. 1996; 33(3):971–96.
  • Valizadeh Z, Ezzati R, Khezerloo S. Approximate symmetric solution of Dual Fuzzy systems regarding two different fuzzy multiplications. Indian Journal of science and Technology. 2012 Feb; 5(2):1–13.
  • Usry R, Rosli R, Maat SM. An error analysis of matriculation students permutations and combinations. Indian Journal of science and Technology. 2016 Jan; 9(4):1–6.
  • Atkinson A, Kendall E. An introduction to numerical Analysis. second edn., John Wiley; 2001.
  • Conte S, Boor C, De D. Elementary Numerical Analysis. Tata Mac-Graw Hill; 1980. p. 1–2. PMid:6892821


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