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Investigation of Errors in Solving Problems for Simple Equations of Mathematical Physics by Iterative Methods

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Abstract

The error caused by inaccuracy in solving systems of equations by iterative methods is investigated. An upper estimate for an axially symmetric heat conduction equation is found for the error accumulated in several time steps. The estimate shows a linear dependence of the error on the threshold value of a criterion for limiting the number of iterations, a quadratic growth of the error depending on the number of points in space, and its independence of the number of steps in time. A computational experiment shows good agreement of the estimate with real errors at boundary and initial conditions of various types. A quadratic growth for Laplace’s equation of the error caused by an accuracy limitation in using an iterative method, depending on the number of points in space \(n\), is found empirically. A growth of \(n^{4}\) for the similar error in the biharmonic equation is found.

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Authors and Affiliations

  1. Ufa State Aviation Technical University, 450000, Ufa, Russia

    V. P. Zhitnikov & N. M. Sherykhalina

  2. Saint Petersburg State University of Civil Aviation, 196210, St. Petersburg, Russia

    R. R. Muksimova

Authors
  1. V. P. Zhitnikov
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  2. N. M. Sherykhalina
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  3. R. R. Muksimova
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Corresponding authors

Correspondence to V. P. Zhitnikov, N. M. Sherykhalina or R. R. Muksimova.

Additional information

Translated from Sibirskii Zhurnal Vychislitel’noi Matematiki, 2021, Vol. 24, No. 2, pp. 131–144.https://doi.org/10.15372/SJNM20210202.

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Zhitnikov, V.P., Sherykhalina, N.M. & Muksimova, R.R. Investigation of Errors in Solving Problems for Simple Equations of Mathematical Physics by Iterative Methods. Numer. Analys. Appl. 14, 115–125 (2021). https://doi.org/10.1134/S1995423921020026

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  • DOI: https://doi.org/10.1134/S1995423921020026

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