If you have a large multivariable ODE system, and certain processes occur at a much smaller time scale, how can you implement a solver that uses smaller time steps for state variables involved in fast processes, and large time steps for state variables involved in slow processes, and ensure the result is still mathematically sound. For simplicity, we assume that we are using the explicit Euler solver method per state variable.

I ask because I am concerned, for example, about ensuring certain quantities remain conserved. There is a lot of literature about variable time step size depending on the error estimation, but I am asking about assuming different time steps for different state variables. This is an optimization to reduce runtime on a computing architecture that does not do well with runtime adaptive time stepping.


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