The Estimation of the Error at Richardson’s Extrapolation and the Numerical Solution of Integral Equations of the Second Kind

DOI: 10.4236/oalib.1102051   PDF   HTML   XML   1,703 Downloads   2,117 Views   Citations

Abstract

The mode of definition of the error at polynomial Richardson’s extrapolation is described. Along with the table of extrapolations the new magnitudes reflecting expediency and efficiency of extrapolation are entered. On concrete examples it is shown that application of Richardson’s extrapolation to a solution of integral equations has appeared rather effective and gives a solution with a high exactitude. Application of formulas of interpolation leads to a solution in the analytical aspect.

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Dobrovolsky, I. (2015) The Estimation of the Error at Richardson’s Extrapolation and the Numerical Solution of Integral Equations of the Second Kind. Open Access Library Journal, 2, 1-7. doi: 10.4236/oalib.1102051.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Richardson, L.F. (1911) The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations with an Application to the Stress in a Masonry Dam. Philosophical Transactions of the Royal Society of London. Series A, 210, 307-357.
[2] Stetter, H.J. (1973) Analysis of Discretization Methods for Ordinary Differential Equations. (Springer Tracts, Vol. 23). Springer, Berlin, Heidelberg and New York.
[3] Polyanin, A.D. and Manzhirov, A.V. (2008) Handbook of Integral Equations. Chapman & Hall/CRC Press, Boca Raton and London.
http://dx.doi.org/10.1201/9781420010558

  
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