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The two-level finite difference schemes for the heat equation with nonlocal initial condition

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  • Martín-Vaquero, Jesús
  • Sajavičius, Svajūnas

Abstract

In this paper, the two-level finite difference schemes for the one-dimensional heat equation with a nonlocal initial condition are analyzed. As the main result, we obtain conditions for the numerical stability of the schemes. In addition, we revise the stability conditions obtained in [21] for the Crank–Nicolson scheme. We present several numerical examples that confirm the theoretical results within linear, as well as nonlinear problems. In some particular cases, it is shown that for small regions of the time step size values, the explicit FTCS scheme is stable while certain implicit methods, such as Crank–Nicolson scheme, are not.

Suggested Citation

  • Martín-Vaquero, Jesús & Sajavičius, Svajūnas, 2019. "The two-level finite difference schemes for the heat equation with nonlocal initial condition," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 166-177.
    • Handle: RePEc:eee:apmaco:v:342:y:2019:i:c:p:166-177
    DOI: 10.1016/j.amc.2018.09.025
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    1. Dennis E. Jackson, 1992. "Error estimates for the semidiscrete finite element approximation of linear nonlocal parabolic equations," International Journal of Stochastic Analysis, Hindawi, vol. 5, pages 1-9, January.
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