The presentation discusses all steps of the procedure, starting from amplitude and

time scaling for a non-dimensional representation and for the identiﬁcation of the

perturbation parameter. Suitable time constants lead to the short term and long term

behaviour, also known as the inner and outer solution. Special attention is paid to the

matching process by the deﬁnition of a suitable intermediate layer. The results are

presented in concise form as a summary of the required calculations. An extended

example compares the zero order and ﬁrst order perturbation approximations for the

short term and long term solution as well as the uniform solution. A comparison to

the numerical solution of the initial set of nonlinear ordinary differential equations

demonstrates the achievable accuracy.},
author = {Kram, Sebastian and Schäfer, Maximilian and Rabenstein, Rudolf},
doi = {10.1007/s10910-017-0848-3},
faupublication = {yes},
journal = {Journal of Mathematical Chemistry},
keywords = {Enzyme kinetics; Perturbation approach; Nonlinear ordinary differential equations},
pages = {1153-1183},
peerreviewed = {Yes},
title = {{Approximation} of enzyme kinetics for high enzyme concentration by a ﬁrst order perturbation approach},
volume = {56},
year = {2018}
}