$$ \newcommand{\uex}{{u_{\small\mbox{e}}}} \newcommand{\Aex}{{A_{\small\mbox{e}}}} \newcommand{\half}{\frac{1}{2}} \newcommand{\Oof}[1]{\mathcal{O}(#1)} $$

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Implementations of variable coefficients; functions

Plain functions:

def a(t):
    return a_0 if t < tp else k*a_0

def b(t):
    return 1

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