model - 计算机上的连续模拟

Question

数字计算机是一个离散系统。那么，是否就不能在数字计算机上模拟连续模型呢？似乎只能通过离散模拟来近似连续模型。从我读到的内容来看，情况似乎是这样，但我想从其他人那里获得关于该主题的一些反馈/意见。

我在搜索有关此主题的更多信息时确实发现了这一点:

Continuous simulation is something that can only really be accomplished with an analog computer. Using a digital computer one can approximate a continuous simulation by making the time step of the simulation sufficiently small so there are no transitions within the system between time steps. The premise for a continuous simulation is that there is a continuous time flow and the simulation is stepped in time increments. ¹

我还认为这对通过离散模拟进行近似提出了一个很好的观点:

In some systems the state changes all the time, not just at the time of some discrete events. For example, the water level in a reservoir with given in and outflows may change all the time. In such cases "continuous simulation" is more appropriate, although discrete event simulation can serve as an approximation. ²

¹ 连续模拟 - http://www.systems-thinking.org/simulation/contsim.htm
² 建模与仿真 - http://home.ubalt.edu/ntsbarsh/simulation/sim.htm

感谢您的输入。

Answer 1

你可能无法使用数字计算机完美地模拟连续系统，但我对建模或模拟连续系统的想法有两个想法:

1. “这是否意味着无法在数字计算机上模拟连续模型？”出于什么目的？它能否完美无瑕地模拟，以便您拥有连续过程的精确数字表示？可能不是。但正如您自己所指出的，离散过程可能足够接近连续过程，以至于它根本无关紧要。
2. 这个过程实际上是连续的吗？我发现在我所在领域的建模中，我遇到了更多被建模为连续过程的过程，而实际上它们应该是离散的(通常是为了利用更简单的分析技术和现成的 ODE 求解器)，而不是遭受不充分离散近似的连续模型。<