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<p>Modified Patankar schemes are linearly implicit time integration methods designed to be unconditionally positive and conservative. In the present work we extend the Patankar-type approach to linear multistep methods and prove that the resulting discretizations retain, with no restrictions on the step size, the positivity of the solution and the linear invariant of the continuous-time system. Moreover, we provide results on arbitrarily high order of convergence and we introduce an embedding technique for the Patankar weights denominators to achieve it.</p>

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Modified Patankar Linear Multistep Methods for Production-Destruction Systems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月5日

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  • Giuseppe Izzo,
  • Eleonora Messina,
  • Mario Pezzella,
  • Antonia Vecchio

摘要

Modified Patankar schemes are linearly implicit time integration methods designed to be unconditionally positive and conservative. In the present work we extend the Patankar-type approach to linear multistep methods and prove that the resulting discretizations retain, with no restrictions on the step size, the positivity of the solution and the linear invariant of the continuous-time system. Moreover, we provide results on arbitrarily high order of convergence and we introduce an embedding technique for the Patankar weights denominators to achieve it.