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I am trying to solve a fourth order partial differential equation $$ {\partial u\over \partial t} = i{\partial^4 u\over \partial x^4} $$ where $i=\sqrt{-1}$ and periodic boundary conditions.

I tried using first order in time and 2nd order in space finite difference scheme, even second order in time and space also. But I am unable to formulate a FD scheme with is stable. I am trying to check stability using von-Neumann stability criteria. Could somebody explain how to proceed in this case?

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  • $\begingroup$ What size $\Delta t$ and $\Delta x$ are you using? Using FD methods on that equation will require painfully small values to be stable $\endgroup$ – Michael Stachowsky May 3 at 16:51
  • $\begingroup$ I am currently using 1e-4 for both space and time. The length of both space and time is 1. But the problem is I can't prove using von-Neumann stability criteria that the scheme is stable $\endgroup$ – Aakash Gupta May 3 at 16:52

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