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Preprint / Mathematical Physics and Mathematics | JINRP112000227 | P112000227 |

Zhidkov, E P ; Soloviev, A G

**Pages: **10 p
**Year: **2000

**Abstract: **
A method for refining approximate eigenvalues and eigenfunctions for a boundaryvalue problem on a halfaxis is suggested. To solve the problem numerically, one has to solve a problem on a finite segment [0,R] instead of the original problem on the interval [0,\infty). This replacement leads to eigenvalues' and eigenfunctions' errors. To choose R beforehand for obtaining their required accuracy is often impossible. Thus, one has to resolve the problem on [0,R] with larger R. If there are two eigenvalues or two eigenfunctions that correspond to different segments, the suggested method allows one to improve the accuracy of the eigenvalue and the eigenfunction for the original problem by means of extrapolation along the segment. This approach is similar to Richardson's method. Moreover, a twoparameter extrapolation is described. It is combination of the extrapolation along the segment and Richardson's extrapolation along a discretization step.

**Web-Page: **
http://www1.jinr.ru/Preprints/2000/p112000227.pdf
**Language: **rus

Record created 2010-10-01, last modified 2014-01-30