Computing the coefficients for the power series solution of the Lane-Emden equation with the Python library SymPy
Klaus Rohe
TL;DR
This paper demonstrates how to use the SymPy library in Python to symbolically compute power series coefficients for the Lane-Emden equation, compare them with numerical solutions, and analyze algorithm performance.
Contribution
It introduces a method for symbolic coefficient calculation of the Lane-Emden equation using SymPy, with performance analysis and comparison to numerical solutions.
Findings
SymPy effectively computes power series coefficients symbolically.
The symbolic solutions closely match numerical solutions.
Algorithm performance metrics are provided.
Abstract
It is shown how the Python library Sympy can be used to compute symbolically the coefficients of the power series solution of the Lane-Emden equation (LEE). Sympy is an open source Python library for symbolic mathematics. The power series solutions are compared to the numerically computed solutions using matplotlib. The results of a run time measurement of the implemented algorithm are discussed at the end.
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Taxonomy
TopicsFractional Differential Equations Solutions · Statistics Education and Methodologies · Model Reduction and Neural Networks