where J (k)=e (k) T Q (k) e (k), e (k)=b k −A x (k), and μ max,ρ are generally selected through experiments to provide the maximum convergence rate preserving steady state misadjustment error small.
The advantages of using a well-balanced scheme in preserving steady states and in resolving small perturbations of such states will be shown.
To conclude this section, the following proposition shows that any emulation, and hence any morphism that is both a reactant morphism and a stoichiomorphism, preserves steady states from the target CRN to the source CRN.
Indeed, the GA scheme is identical to the ROA scheme with the exception of that the GA scheme does not require every node to be updated m times before any node is updated m + 1 times; as steady states are consistent across all dynamic update schemes, this nuance does not alter the effect of edge modifications in the context of preserving steady states.
The method for model reduction used here, balanced residualisation, reduces states while preserving steady-state behaviour.
The proposed scheme is capable of exactly preserving steady-state solutions expressed in terms of a nonlocal equilibrium variable.
We compare the numerical method with an exact solution of the Riemann problem and we check that the method preserves steady-state situations even if we use a discontinuous jump for the porosity.
The distinct basal and prandial characteristics of the IDeg and IAsp components of IDegAsp, which are preserved at steady state (SS) in subjects with T1DM [ 9], help to reduce the risk of hypoglycaemia compared with standard premix insulins such as biphasic insulin apart 30 (BIAsp 30) [ 10].
In this paper, inspired by micro-macro decomposition methods for kinetic equations, we present a class of schemes which are capable to preserve the steady state solution and achieve high order accuracy for a class of time dependent partial differential equations including nonlinear diffusion equations and kinetic equations.
Many numerical methods (e.g., fractional step methods) have difficulty preserving such steady states and cannot accurately calculate small perturbations of such states.
