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The Conjugate Gradient Method for the Dirichlet Problem and Its Modifications

  • V. I. Vasil’evEmail author
  • A. M. KardashevskyEmail author
  • V. V. PopovEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)

Abstract

In this paper we consider a numerical solution of the non-classical Dirichlet problem and its modifications for the second-order two-dimensional hyperbolic equations. In order to determine the missing initial condition using an additional condition specified at the final time, an iterative method of conjugate gradient is used. A direct problem is numerically realized at each iteration. The efficiency of the proposed computational algorithm is confirmed by calculations for model two-dimensional problems.

Keywords

Hyperbolic equation Inverse problem Dirichlet problem Finite difference method Iterative method Conjugate gradients method Random errors 

Notes

Acknowledgments

Supported by mega-grant of the Russian Federation Government (14.Y26.31.0013) and Grant of the Russian Foundation for Basic Research (17-01-00732).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.North-Eastern Federal UniversityYakutskRussia

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