在MATLAB中解决ODES,9:MATLAB ODE SUITE
来自该系列:Solving ODEs in MATLAB
The MATLAB documentation provides two charts summarizing the features of each of the seven functions in the MATLAB ODE suite.
We can get to documentation for the MATLAB ODE Suite by entering this command at the MATLAB prompt-- doc ode45. This will bring us to an extensive documentation for MATLAB ode45 that includes among other things this chart that compares MATLAB ODE solvers. There are seven of them and this compares their various attributes. As we've said before, MATLAB ode45 is the workhorse. It's a nonstiff solver with medium accuracy that is the first one you should try, and we use it most of the time.
我心中有一颗柔软的心脏ode23。它是一个非固定求解器,精度较低,但其精度适合图形工作,因为它选择的步骤尺寸适合大多数图形工作。MATLAB ODE113我们尚未谈论它,这里的1和13之间可能会有一个逗号,因为这是一个可变顺序方法,该顺序从1到13。历史。
If, you know about these things, it's an Adams-Moulton method. I associate this with worked done at Jet Propulsion Laboratory years ago for computing orbits of planets and satellites, which of course are very smooth and go on for years. It can have very high accuracy requirements.
然后是僵硬的求解器。其中有四个-15s,23s和双胞胎,即梯形规则。15s是主要的刚性求解器,低至中等精度。如果您发现ODE45很慢,请采取很多步骤 - 表明问题很严重 - 尝试15s。
23S可以作为低订单方法,低精度,并且以粗误差公差使用。我们没有谈论大规模矩阵。这是衍生术语前面有一个矩阵的地方,可以与恒定的质量矩阵一起使用。然后,以其名称为t的两个例程是基于梯形规则,它们可用于无需任何数值阻尼的问题。您可以查看文档以获取有关梯形方法的更多详细信息。
那就是MATLAB ODE SUITE七个求解器,三个用于非固定问题,四个用于严重问题。您可能永远不会使用任何东西,但是ODE45可能会满足您的所有需求。
There's a second chart in the documentation that summarizes all the options that are available through the ODE Set function. We've briefly mentioned the tolerances, RelTol and AbsTol-- the output function-- these are available in all seven of the solvers.
还有其他各种功能 - 其他各种选项 - 可用于更专业的工作,包括活动处理,为僵硬的求解器提供了雅各布,因此他们不必那么努力地进行数值差异,与大众矩阵相关的选项,提供步骤大小的限制。这些都是我们所有的选项,可以通过ODE设置来指定与ODE求解器进行更专业的工作。
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