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Matrix numerical integration algorithm

  • Numerical Methods, Investigation and Solution of Equations
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Abstract

Algorithms to calculate the weights of quadrature formulas for regular, weakly singular, and singular integrals are constructed and analyzed. The algorithms are easily realized by computer for any number, multiplicity, and distribution of quadrature nodes, and for systems of power, trigonometric, and hyperbolic basis functions as well as a given strictly monotone function used as the integration variable.

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References

  1. A. F. Kalaida, High-Rank Collocation Approximations and Matrix Algorithms of Numerical Differentiation and Integration [in Russian], Unpublished manuscript, VINITI 31.12.82, No. 6562, Kiev (1982).

  2. A. F. Kalaida, Matrix Algorithms for Approximate and Numerical Integration [in Russian], Unpublished manuscript, VINITI 09.07.82, No. 3672, Kiev (1982).

  3. A. F. Kalaida, Matrix Algorithms for Numerical Differentiation and Integration of Discontinuous Functions [in Russian], Unpublished manuscript, VINITI 16.11.82, No. 5607, Kiev (1982).

  4. A. F. Kalaida, Matrix Algorithms for Numerical Differentiation Using Powers of Monotone Basis Functions [in Russian], Unpublished manuscript, UkrNIINTI 25.05.84, No. 915, Kiev (1984).

  5. A. F. Kalaida, Unremovable Error of Matrix Numerical Differentiation and Integration Algorithms [in Russian], Unpublished manuscript, VINITI 31.12.82, No. 6561, Kiev (1982).

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Authors
  1. A. F. Kalaida
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Additional information

Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 68, pp. 3–14, 1989.

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Kalaida, A.F. Matrix numerical integration algorithm. J Math Sci 69, 1369–1378 (1994). https://doi.org/10.1007/BF01250578

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  • DOI: https://doi.org/10.1007/BF01250578

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