The ‘equation-free toolbox’ empowers the computer-assisted analysis of complex, multiscale systems. Its aim is to enable scientists and engineers to immediately use microscopic simulators to perform macro-scale system level tasks and analysis, because micro-scale simulations are often the best available description of a system. The methodology bypasses the derivation of macroscopic evolution equations by computing the micro-scale simulator only over short bursts in time on small patches in space, with bursts and patches well-separated in time and space respectively. We introduce the suite of coded equation-free functions in an accessible way, link to more detailed descriptions, discuss their mathematical support, and introduce a novel and efficient algorithm for Projective Integration. Some facets of toolbox development of equation-free functions are then detailed. Download the toolbox functions and use to empower efficient and accurate simulation in a wide range of science and engineering problems.

“无方程式工具箱”使计算机辅助分析复杂的多尺度系统成为可能。其目的是使科学家和工程师能够立即使用微观仿真器执行宏观系统级的任务和分析，因为微观仿真通常是对系统的最佳描述。该方法通过仅在空间中的小块上的短时间突发上计算微型模拟器，从而绕开了宏观演化方程的推导，而突发和块在时间和空间上分别很好地分离。我们以一种易于访问的方式介绍了无编码方程式函数套件，链接到更详细的描述，讨论了它们的数学支持，并介绍了一种新颖高效的投影积分算法。然后详细介绍了无方程式函数工具箱开发的一些方面。下载工具箱功能并使用它来实现各种科学和工程问题中的高效，准确的仿真。