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Accurate dense output formula for exponential integrators using the scaling and squaring method. (English) Zbl 1315.65065

Summary: This paper proposes an accurate dense output formula for exponential integrators. The computation of matrix exponential function is a vital step in implementing exponential integrators. By scrutinizing the computational process of matrix exponentials using the scaling and squaring method, valuable intermediate results in this process are identified and then used to establish a dense output formula. Efficient computation of dense outputs by the proposed formula enables time integration methods to set their simulation step sizes more flexibly. The efficacy of the proposed formula is verified through numerical examples from the power engineering field.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L04 Numerical methods for stiff equations

Software:

MATLAB expm
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Full Text: DOI

References:

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