NodePy (Numerical ODEs in Python) is a Python package for designing, analyzing, and testing numerical methods for initial value ODEs. Its development was motivated by my own research in time integration methods for PDEs. I found that I was frequently repeating tasks that could be automated and integrated. Initially I developed a collection of MATLAB scripts, but this became unwieldy due to the large number of files that were necessary and the more limited capability for code reuse. NodePy represents an object-oriented approach, in which the basic object is a numerical ODE solver. The idea is to design a laboratory for such methods in the same sense that MATLAB is a laboratory for matrices. Some distinctive design goals are: Plug-and-play: any method can be applied to any problem using the same syntax. Also, properties of different kinds of methods are available through the same syntax. This makes it easy to compare different methods. Abstract representations: Generally, the most abstract (hence powerful) representaton of an object is used whenever possible. Thus, order conditions are generated using products on rooted trees (or other recursions) rather than being hard-coded. Numerical representation: The most precise representation possible is used for quantities such as coefficients: rational numbers (using SymPy’s Rational class) when available, floating-point numbers otherwise. Where necessary, method properties are determined by numerical calculations, using appropriate tolerances. Thus the “order” of a method with floating-point coefficients is determined by checking whether the order conditions are satisfied to within a small value (near machine-epsilon). For efficiency reasons, coefficients are always converted to floating-point for purposes of applying the method to a problem.

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