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| We consider the computation of the flow of partial differential equations that can be discretized as $\partial_t u = (A+\epsilon B)u$.
The flow corresponds to the matrix exponential $\exp(A+\epsilon B)$, where $A$ is cheaply diagonalizable (for example by Fourier transforms) and the perturbation $B$ is a dense matrix with $|\varepsilon|\ll 1$. After proper design and application, higher order splitting methods have been found to be superior to standard methods for certain classes of perturbed matrices. |
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