Schur Decomposition for Stiff Differential Equations
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A quantitative definition of numerical stiffness for initial value problems is proposed. Exponential integrators can effectively integrate linearly stiff systems, but they become expensive when the linear coefficient is a matrix, especially when the time step is adapted to maintain a prescribed local error. Schur decomposition is shown to avoid the need for computing matrix exponentials in such simulations, while still circumventing linear stiffness.
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