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

In: Approximation and Computation

Author

Listed:
  • Dejan R. Bojović

    (University of Kragujevac)

  • Boško S. Jovanović

    (University of Belgrade)

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.

Suggested Citation

  • Dejan R. Bojović & Boško S. Jovanović, 2010. "Finite Difference Method for a Parabolic Problem with Concentrated Capacity and Time-Dependent Operator," Springer Optimization and Its Applications, in: Walter Gautschi & Giuseppe Mastroianni & Themistocles M. Rassias (ed.), Approximation and Computation, pages 285-296, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-6594-3_18
    DOI: 10.1007/978-1-4419-6594-3_18
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