Title: Efficiently and easily integrating differential equations with JiTCODE, JiTCDDE, and JiTCSDE,
Abstract: We present a family of Python modules for the numerical integration of
ordinary, delay, or stochastic differential equations. The key features are
that the user enters the derivative symbolically and it is
just-in-time-compiled, allowing the user to efficiently integrate differential
equations from a higher-level interpreted language. The presented modules are
particularly suited for large systems of differential equations such as used to
describe dynamics on complex networks. Through the selected method of input,
the presented modules also allow to almost completely automatize the process of
estimating regular as well as transversal Lyapunov exponents for ordinary and
delay differential equations. We conceptually discuss the modules' design,
analyze their performance, and demonstrate their capabilities by application to
timely problems.