Higher-order compact finite difference method for a free boundary problem of ductal carcinoma in situ

Komal Deswal, Komal Taneja and Devendra Kumar

Applied Mathematics and Computation, 2024, vol. 467, issue C

Abstract: A higher-order compact finite difference scheme is established to investigate the model of ductal carcinoma in situ, a free boundary value problem. For the first time, to determine the growth of a tumor numerically, a compact finite difference method is applied in the spatial direction, and the Crank-Nicolson scheme is used in the temporal direction. Through stability analysis, it has been demonstrated that the proposed numerical scheme is unconditionally stable. The convergence of the numerical scheme is analyzed theoretically by von Neumann's method. It has been proved that the proposed numerical method is second-order convergent in time and fourth-order convergent in space in the L2-norm. Two numerical examples are provided to verify the scheme's efficiency and validate the theoretical results. The tabular and graphical representations confirm the high accuracy and adaptability of the scheme.

Keywords: Compact finite difference method; Crank-Nicolson method; Ductal carcinoma in situ; Free boundary problem; von-Neumann's method (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:467:y:2024:i:c:s0096300323006707

DOI: 10.1016/j.amc.2023.128501

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