A numerical scheme for solving nonlinear backward parabolic problems

Document Type: Research Paper

Authors

Faculty of Mathematics‎, ‎K‎. ‎N‎. ‎Toosi University of Technology‎, ‎Tehran‎, ‎Iran

Abstract

‎In this paper a nonlinear backward parabolic problem in one‎ ‎dimensional space is considered‎. ‎Using a suitable iterative‎ ‎algorithm‎, ‎the problem is converted to a linear backward parabolic‎ ‎problem‎. ‎For the corresponding problem‎, ‎the backward finite‎ ‎differences method with suitable grid size is applied‎. ‎It is shown‎ ‎that if the coefficients satisfy some special conditions‎, ‎this‎ ‎algorithm not only is convergent‎, ‎but also is conditionally‎ ‎stable‎. ‎Moreover‎, ‎it is proved that the estimated values converge‎ ‎to the exact solution of the problem‎. ‎Al these‎ ‎approaches examined in some numerical examples. corresponding‎ ‎theorems for the convergency and stability of the solution are‎ ‎studied‎.

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Volume 41, Issue 6
November and December 2015
Pages 1453-1464
  • Receive Date: 11 November 2013
  • Revise Date: 10 September 2014
  • Accept Date: 11 September 2014