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Multiscaling analysis of a slowly varying anaerobic digestion model
Author(s) -
Alsharidi Abdulaziz K.,
Khan Ashfaq A.,
Shepherd John J.,
Stacey Andrew J.
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6315
Subject(s) - limiting , mathematics , nonlinear system , anaerobic digestion , range (aeronautics) , statistical physics , numerical analysis , steady state (chemistry) , mathematical analysis , physics , chemistry , methane , mechanical engineering , materials science , organic chemistry , quantum mechanics , engineering , composite material
We construct the slowly varying limiting state solutions to a nonlinear dynamical system for anaerobic digestion with Monod‐based kinetics involving slowly varying model parameters arising from slow environmental variation. The advantage of these approximate solutions over numerical solutions is their applicability to a wide range of parameter values. We use these limiting state solutions to develop analytic approximations to the full nonlinear system by applying a multiscaling technique. The approximate solutions are shown to compare favorably with numerical solutions.