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When beginning coding projects, consider your mindset. For example, if you are most comfortable beginning new tasks with all future steps carefully planned, you may benefit from starting your projects with pseudocode. Pseudocode is a list of plain language descriptions for operations you plan to complete, which you will write out in a document and later translate line by line into code. A benefit of this method is that it allows you to conceptualize your project from start to finish and provides a discrete goal for each line of code that you will write. If you are more comfortable learning by doing, you may prefer to write code directly, observing the output of each line and commenting in the text what your last line completed, reaching the end goal in smaller increments. In both cases, it is important to comment your code throughout to ensure that future-you can understand what present-you was thinking.

As we have shown in the Using SoS workflow system in Jupyter and from command line and the following tutorials, SoS allows you to perform your data analysis in Jupyter or record the scripts you developed in other environments in a Jupyter notebook, without a steep learning curve.

The multi-language data analysis can be converted almost trivially to the following SoS workflow. In contrast to analysis in SoS notebook, each step must contain complete scripts that can be executed independent of other steps. One of the benfits of the conversion is that the workflow can be execute from command line.

Now that you have learned the basics of SoS, you can go ahead and use them to oraganize your scripts. However, SoS is very powerful system and can be used to write powerful workflows and execute scripts in containers and remote hosts. The following example from How to define and execute basic SoS workflows demonstrates the creation and passing of substeps and you can learn more from other tutorials.

In the context of multi-scale waves, the dedicated methods chosen for each subsystem are then responsible for dealing with the fastest scales associated with each one of them, in a separate manner; then, the composition of the global solution based on the splitting scheme should guarantee the good description of the global physical coupling. A rigorous numerical analysis is therefore required to better establish the conditions for which the latter fundamental constraint is verified. As a matter of fact, several works [4, 5, 1] proved that the standard numerical analysis of splitting schemes fails in the presence of scales much faster than the splitting time step and motivated more rigorous studies for these stiff configurations [6, 7] and in the case where spatial multi-scale phenomena arise as a consequence of steep spatial gradients [8].

On the other hand, one must also take into account possible order reductions coming this time from space multi-scale phenomena due to steep spatial gradients whenever large splitting time steps are considered, as analyzed in [8]:

Figure 1 shows that both Lie and Strang schemes have asymptoticly local order 2 and 3 for small time steps. Nevertheless, for larger time steps, previous studies in [6] and [8] describe better the numerical behavior of these schemes. For , order drops to as predicted by (7); whereas for , we see the influence of spatial gradients as predicted by (11) and thus, order is recovered after some transition phase. Same conclusions are drawn for Strang schemes, order of drops from to according to (8), while for , we see the influence of steep spatial gradients that alter the order given by (10). Maximum error considers the maximum value between computed normalized local errors for , and variables; in these numerical tests, it corresponds to variable . Finally, in all cases the reaction ending schemes show better behaviors for larger splitting time steps, according to [6]. In particular, behaves even better than , whereas is the best alternative for all time steps.

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