A backward differentiation formula (BDF) has been shown to be an effective way to\nsolve a system of ordinary differential equations (ODEs) that have some degree of\nstiffness. However, sometimes, due to high-frequency variations in the external time\nseries of boundary conditions, a small time-step is required to solve the ODE system\nthroughout the entire simulation period, which can lead to a high computational\ncost, slower response, and need for more memory resources. One possible strategy to\novercome this problem is to dynamically adjust the time-step with respect to the system�s\nstiffness. Therefore, small time-steps can be applied when needed, and larger\ntime-steps can be used when allowable. This paper presents a new algorithm for adjusting\nthe dynamic time-step based on a BDF discretization method. The parameters\nused to dynamically adjust the size of the time-step can be optimally specified to\nresult in a minimum computation time and reasonable accuracy for a particular case\nof ODEs. The proposed algorithm was applied to solve the system of ODEs obtained\nfrom an activated sludge model (ASM) for biological wastewater treatment processes.\nThe algorithm was tested for various solver parameters, and the optimum set of three\nadjustable parameters that represented minimum computation time was identified.\nIn addition, the accuracy of the algorithm was evaluated for various sets of solver\nparameters.
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