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This study discretizes a continuous-time smoking model using the standard forward Euler and non-standard finite difference (NSFD) schemes. The dynamical properties of both systems are compared to the original continuous model and it is found that the NSFD system remains positive for all positive initial values and has the same fixed points and local stability properties as the continuous model. In contrast, the dynamics of the Euler system is contingent on the step size and may allow numerical instabilities. In the end, numerical investigations are carried out to support the theoretical findings and highlight the benefits of the NSFD scheme compared to the conventional Euler method.

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Discretization of a Smoking Model: A Comparison of Euler and NSFD Schemes

  • 会议论文

  • 发表日期：

    2026年

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  • Tapan Sarkar,
  • Saduri Das,
  • Sanuwar Ahmed Choudhury,
  • Pankaj Biswas

摘要

This study discretizes a continuous-time smoking model using the standard forward Euler and non-standard finite difference (NSFD) schemes. The dynamical properties of both systems are compared to the original continuous model and it is found that the NSFD system remains positive for all positive initial values and has the same fixed points and local stability properties as the continuous model. In contrast, the dynamics of the Euler system is contingent on the step size and may allow numerical instabilities. In the end, numerical investigations are carried out to support the theoretical findings and highlight the benefits of the NSFD scheme compared to the conventional Euler method.