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

Jesús Martín-Vaquero and Svajūnas Sajavičius

Applied Mathematics and Computation, 2019, vol. 342, issue C, 166-177

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.

Keywords: Heat equation; Nonlocal initial condition; Finite difference scheme; Stability; Convergence (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:342:y:2019:i:c:p:166-177

DOI: 10.1016/j.amc.2018.09.025

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