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For questions about explicit differential equation algorithms, that directly relate the next time step of some variable y to some function of y at the current time step.

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Why do I get an oscillatory solution when applying the implicit trapezoidal method to the li...

I think you might have mixed up some terminology. An exponential integrator would use some type of eigensolver or related approach to exactly calculate $$f^{n + 1} = e^{\delta t\cdot \mathcal A}f^n$$ …
Daniel Shapero's user avatar