Fast Runge-Kutta approximation of inhomogeneous parabolic equations

Abstract

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 $$O\left(\log N\log \frac{1}{\epsilon }\right)$$ linear systems of equations. We derive, analyse, and numerically illustrate this fast algorithm.

References in corpus (2)

• Fast and oblivious convolution quadrature
• A spectral order method for inverting sectorial Laplace transforms

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