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 weight denominators to achieve it.

翻译：修正Patankar格式是一类线性隐式时间积分方法，其设计目标为无条件保持正性与守恒性。本文将该类Patankar方法推广至线性多步法，并证明所得离散格式在任意步长下均能保持连续时间系统的解的正性及线性不变量。此外，我们给出了任意高阶收敛性的理论结果，并引入基于Patankar权重分母的嵌入技术以实现该收敛阶。