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An algorithm for numerical integration based on quasi-interpolating splines

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Abstract

In this paper product quadratures based on quasi-interpolating splines are proposed for the numerical evaluation of integrals with anL 1-kernel and of Cauchy Principal Value integrals.

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References

  1. A. Alaylioglu, D.S. Lubinsky and D. Eyre, Product integration of logarithmic singular integrands based on cubic splines, J. Comp. Appl. Math. 11 (1984) 353–366.

    Google Scholar 

  2. C. Dagnino and A. Palamara Orsi, Product integration of piecewise continuous integrands based on cubic spline interpolation at equally spaced nodes, Numer. Math. 52 (1988) 459–466.

    Google Scholar 

  3. C. Dagnino, Product integration of singular integrands based on cubic spline interpolation at equally spaced nodes, Numer. Math. 57 (1990) 97–104.

    Google Scholar 

  4. C. Dagnino and E. Santi, On the evaluation of one-dimensional Cauchy principal value integrals by rules based on cubic spline interpolation. Computing 43 (1990) 267–276.

    Google Scholar 

  5. C. Dagnino and E. Santi, Spline product quadrature rules for Cauchy singular integrals, J. Comp. Appl. Math. 33 (1990) 133–140.

    Google Scholar 

  6. C. Dagnino and E. Santi, On the convergence of spline product rules for Cauchy principal value integrals, J. Comp. Appl. Math. 36 (1991) 181–187.

    Google Scholar 

  7. C. Dagnino, V. Demichelis and E. Santi, Numerical integration based on quasi-interpolating splines, Computing 50 (1993) 149–163.

    Google Scholar 

  8. C. Dagnino and P. Rabinowitz, Product integration of singular integrands using quasiinterpolating splines, submitted for publication (1992).

  9. C. Dagnino, V. Demichelis and E. Santi, A FORTRAN code for computing nodes and weights of quadratures based on quasi-interpolating splines, Int. Report (1992).

  10. P.J. Davis and P. Rabinowitz,Numerical Integration, 2nd ed. (Academic Press, New York, 1984).

    Google Scholar 

  11. C. de Boor,A Practical Guide to Splines, Applied Mathematical Sciences, vol. 27 (Springer, New York, 1978).

    Google Scholar 

  12. A. Gerasoulis, Piecewise-polynomial quadratures for Cauchy singular integrals, SIAM J. Numer. Anal. 23 (1986) 891–902.

    Google Scholar 

  13. T.N.E. Greville, Spline functions, interpolation and numerical quadrature, in:Mathematical Methods for Digital Computers, Vol. 2, eds. A. Ralston and H.S. Wolf (Wiley, New York, 1967) pp. 156–168.

    Google Scholar 

  14. T. Lyche and L.L. Schumaker, Local spline approximation methods, J. Approx. Theory 15 (1975) 294–325.

    Google Scholar 

  15. P. Rabinowitz, The convergence of non-interpolatory product integration rules, in:Numerical Integration (Reidel, 1987).

  16. P. Rabinowitz, Numerical integration based on approximating splines, J. Comp. Appl. Math. 33 (1990) 73–83.

    Google Scholar 

  17. L.L. Schumaker,Spline Functions (Wiley, 1981).

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Work sponsored by “Ministero dell'Università e Ricerca Scientifica” of Italy.

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Dagnino, C., Demichelis, V. & Santi, E. An algorithm for numerical integration based on quasi-interpolating splines. Numer Algor 5, 443–452 (1993). https://doi.org/10.1007/BF02109185

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