Back
 OALibJ  Vol.2 No.11 , November 2015
The Estimation of the Error at Richardson’s Extrapolation and the Numerical Solution of Integral Equations of the Second Kind
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.
Cite this paper: 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.
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

 
 
Top