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

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  • Deswal, Komal
  • Taneja, Komal
  • Kumar, Devendra

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.

Suggested Citation

  • Deswal, Komal & Taneja, Komal & Kumar, Devendra, 2024. "Higher-order compact finite difference method for a free boundary problem of ductal carcinoma in situ," Applied Mathematics and Computation, Elsevier, vol. 467(C).
    • Handle: RePEc:eee:apmaco:v:467:y:2024:i:c:s0096300323006707
    DOI: 10.1016/j.amc.2023.128501
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    1. Mahmood, Mohammed Shuker & Mahmood, Silvia & Dobrota, DuĊĦan, 2010. "A numerical algorithm for avascular tumor growth model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(6), pages 1269-1277.
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