Finite Difference Method for a Parabolic Problem with Concentrated Capacity and Time-Dependent Operator

Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 42)

Abstract

We investigate the convergence of difference schemes for the one-dimensional heat equation with a time-dependent operator and the coefficient of the time derivative containing a Dirac delta distribution. An abstract operator method is developed for analyzing this equation. An estimate of the rate of convergence in a special discrete energetic \widetilde{W}2 2, 1 Sobolev norm, compatible with the smoothness of the solution, is obtained.

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Notes

Acknowledgements

This research was supported by the Ministry of Science of the Republic of Serbia under project # 144005A.

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Faculty of ScienceUniversity of KragujevacKragujevacSerbia
  2. 2.Faculty of MathematicsUniversity of BelgradeBelgradeSerbia

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