The following equation $$\partial_t U = i\partial_x^2U$$ can be solved using a step-wise Fourier transformation method: $$U(x, t+\Delta t) = F^{-1}\left(\exp(i\cdot \Delta t\cdot k^2)F(U(x, t))\right)$$ But is it possible to apply the same method to an extended equation, which looks like $$\partial_t^2U+\partial_tU=i\partial_x^2 U$$ and if yes, how?
2026-04-18 22:24:43.1776551083
Fourier Step method for combined time derivative
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