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Mathematics of Computation

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Finite difference solution of a nonlinear Klein-Gordon equation with an external source
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by G. Berikelashvili, O. Jokhadze, S. Kharibegashvili and B. Midodashvili PDF
Math. Comp. 80 (2011), 847-862 Request permission

Abstract:

In this paper, we consider the Darboux problem for a (1+1)-dimensional cubic nonlinear Klein-Gordon equation with an external source. Stable finite difference scheme is constructed on a four-point stencil, which does not require additional iterations for passing from one level to another. It is proved, that the finite difference scheme converges with the rate $O(h^2)$, when the exact solution belongs to the Sobolev space $W_2^2$.
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Additional Information
  • G. Berikelashvili
  • Affiliation: A. Razmadze Mathematical Institute, 1 M. Aleksidze str., 0193, Tbilisi, Georgia
  • Email: bergi@rmi.acnet.ge
  • O. Jokhadze
  • Affiliation: A. Razmadze Mathematical Institute, 1 M. Aleksidze str., 0193, Tbilisi, Georgia
  • Email: ojokhadze@yahoo.com
  • S. Kharibegashvili
  • Affiliation: A. Razmadze Mathematical Institute, 1 M. Aleksidze str., 0193, Tbilisi, Georgia
  • Email: khar@rmi.acnet.ge
  • B. Midodashvili
  • Affiliation: I. Javakhishvili Tbilisi State University, 2, University str., 0186, Tbilisi, Georgia
  • Email: bidmid@hotmail.com
  • Received by editor(s): May 13, 2008
  • Received by editor(s) in revised form: February 4, 2010
  • Published electronically: August 25, 2010
  • © Copyright 2010 American Mathematical Society
  • Journal: Math. Comp. 80 (2011), 847-862
  • MSC (2010): Primary 65M06, 35L70
  • DOI: https://doi.org/10.1090/S0025-5718-2010-02416-0
  • MathSciNet review: 2772098