Fast Runge-Kutta approximation of inhomogeneous parabolic equations

The result after $N$ steps of an implicit Runge-Kutta time discretization of an inhomogeneous linear parabolic differential equation is computed, up to accuracy $ε$, by solving only $O\Big(\log N \log \frac1ε\Big)$ linear systems of equations. We derive, analyse, and numerically illustrate this fast algorithm.

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