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Does anyone know how to use time filter with a system of equations like

  1. $i\dot{\phi} = \chi$
  2. $i \dot{\chi} = - f(\phi)?$

I looked up higher order Robert Asselin filter but the only example I found was a single linear equation however in the original paper in which it was proposed, it was proposed for a general equation but without any nonlinear example.

Any help would be appreciated.

Adrian Keister
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Sachin Vaidya
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  • Don't know if it's helpful or not, but you can integrate this equation once to obtain $$\left(\dot{\phi}\right)^{!2}=2\int f(\phi),d\phi+C.$$ – Adrian Keister Feb 12 '21 at 20:06
  • @AdrianKeister thanks. But actually I’m not sure how this can be used. And also the equations mentioned here are simplified versions. Actually phi and chi have indices and f(phi) contains laplacian and nonlinear terms dependent on multiple phi’s that exist in the problem. Actually I just want to figure out a way to implement some time filter algorithm so that I can prevent the oscillations (in the conserved quantities) from growing – Sachin Vaidya Feb 13 '21 at 05:22

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