Effective high order integrators for linear Klein-Gordon equations in low to highly oscillatory regimes
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We introduce an efficient class of high order schemes for the Klein–Gordon equation from low to high frequency regimes. The new schemes resolve the oscillations triggered by the input term and allow for second order convergence in time uniformly in the high frequencies ω_n and fourth order convergence under the natural scaling Δ t ∼ 1/√(|ω_n|). The construction is based on Magnus expansions tailored to the structure of the input term. Numerically experiments underline our theoretical findings and show the efficiency of the new schemes.
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