Fast Runge-Kutta approximation of inhomogeneous parabolic equations

Details Fast Runge-Kutta approximation of inhomogeneous parabolic equations Fast Runge-Kutta approximation of inhomogeneous parabolic equations

2005-04-22

arxiv.org/abs/math/0504466v1

Numer. Math., Vol. 102, (2), 277 - 291, (2005)

Mathematics

Numerical Analysis

Scientific paper

10.1007/s00211-005-0624-3

The result after $N$ steps of an implicit Runge-Kutta time discretization of
an inhomogeneous linear parabolic differential equation is computed, up to
accuracy $\epsilon$, by solving only $$O\Big(\log N \log \frac1\epsilon \Big)
$$ linear systems of equations. We derive, analyse, and numerically illustrate
this fast algorithm.

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