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首页> 外文期刊>Journal of Economic Dynamics and Control >Steady-state invariance in high-order Runge-Kutta discretization of optimal growth models
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Steady-state invariance in high-order Runge-Kutta discretization of optimal growth models

机译：最优增长模型的高阶Runge-Kutta离散化中的稳态不变性

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摘要

This work deals with infinite horizon optimal growth models and uses the results in the Mercenier and Michel (1994a) paper as a starting point. Mercenier and Michel (1994a) provide a one-stage Runge-Kutta discretization of the above-mentioned models which preserves the steady state of the theoretical solution. They call this feature the "steady-state invariance property". We generalize the result of their study by considering discrete models arising from the adoption of s-stage Runge-Kutta schemes. We show that the steady-state invariance property requires two different Runge-Kutta schemes for approximating the state variables and the exponential term in the objective function. This kind of discretization is well-known in literature as a partitioned symplectic Runge-Kutta scheme. Its main consequence is that it is possible to rely on the well-stated theory of order for considering more accurate methods which generalize the first order Mercenier and Michel algorithm. Numerical examples show the efficiency and accuracy of the proposed methods up to the fourth order, when applied to test models.
机译：这项工作涉及无限地平线最优增长模型，并以Mercenier和Michel（1994a）论文中的结果为起点。 Mercenier和Michel（1994a）提供了上述模型的一阶段Runge-Kutta离散化，该离散化保留了理论解的稳态。他们称此功能为“稳态不变性”。我们通过考虑采用s阶段Runge-Kutta方案产生的离散模型来概括他们的研究结果。我们表明，稳态不变性需要两种不同的Runge-Kutta方案来近似目标函数中的状态变量和指数项。这种离散化在文献中被称为分区辛格Runge-Kutta方案。它的主要结果是，可以依靠成熟的顺序理论来考虑更精确的方法，这些方法可以对一阶Mercenier和Michel算法进行泛化。数值算例表明了该方法在测试模型中的有效性和准确性，最高可达四阶。

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