Instead of focusing on efficiency, they key for this group is to have a clear and neatly defined (universal) interface which has a lot of flexibility. The idea is pretty simple: users of a problem solving environment (the examples from his papers are MATLAB and Maple) do not have the same requirements as more general users of scientific computing. Shampine also had a few other papers at this time developing the idea of a “methods for a problem solving environment” or a PSE. MATLAB’s differential equation solver suite was described in a research paper by its creator Lawerance Shampine, and this paper is one of the most highly cited SIAM Scientific Computing publications.
You can find it here (click for PDF):ĭue to its popularity, let’s start with MATLAB’s built in differential equation solvers. If you just want a quick summary, I created a table which has all of this information.
#DIFFERENTIAL EQUATION MATHEMATICA HOW TO#
You will see at the end that DifferentialEquations.jl does offer pretty much everything from the other suite combined, but that’s no accident: our software organization came last and we used these suites as a guiding hand for how to design ours.) Quick Summary Table (Full disclosure, I am the lead developer of DifferentialEquations.jl. I hope that by giving you the details for how each suite was put together (and the “why”, as gathered from software publications) you can come to your own conclusion as to which suites are right for you. This is a good way to reflect upon what’s available and find out where there is room for improvement. What I would like to do is take the time to compare and contrast between the most popular offerings. For the field of scientific computing, the methods for solving differential equations are what’s important.
Many times a scientist is choosing a programming language or a software for a specific purpose.
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