Schur Decomposition for Stiff Differential Equations

05/21/2023

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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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Schur Decomposition for Stiff Differential Equations

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Schur Decomposition for Stiff Differential Equations

Related Research

Exponential integrators for large-scale stiff matrix Riccati differential equations

Computing the Lyapunov operator φ-functions, with an application to matrix-valued exponential integrators

A new symmetric linearly implicit exponential integrator preserving polynomial invariants or Lyapunov functions for conservative or dissipative systems

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