Skip to main content
Log in

On the convergence of finite difference schemes for the heat equation with concentrated capacity

  • Original article
  • Published:
Numerische Mathematik Aims and scope Submit manuscript

Summary.

We investigate the convergence of difference schemes for the one-dimensional heat equation when the coefficient at the time derivative (heat capacity) is \(c\left( x\right) =1+K\delta \left( x-\xi \right). K = \const > 0\) represents the magnitude of the heat capacity concentrated at the point \(x=\xi\). An abstract operator method is developed for analyzing this equation. Estimates for the rate of convergence in special discrete energetic Sobolev's norms, compatible with the smoothness of the solution are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Additional information

Received November 2, 1999 / Revised version received July 24, 2000 / Published online May 4, 2001

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jovanovic, B., Vulkov, L. On the convergence of finite difference schemes for the heat equation with concentrated capacity. Numer. Math. 89, 715–734 (2001). https://doi.org/10.1007/s002110100280

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s002110100280

Navigation