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=== Local Linearization schemes ===
[[File:Figure DDE.png|thumb|450x450px|'''Fig. 2''' Approximate paths of the [https://doi.org/10.1016/S0022-5193(05)80142-0 Marchuk et al. (1991)] antiviral immune model described by a stiff system of ten-dimensional nonlinear DDEs with five time delays: top, continuous Runge-Kutta (2,3) scheme ; botom, LL scheme (5.3). Step-size ''h=0.01'' fixed, and ''p=q=6''.]]
Depending of the approximations <math>\widetilde{\mathbf{z}}_{t_{n}}^{i}</math> and of the algorithm to compute <math>\mathbf{\phi }</math> different Local Linearizations schemes can be defined. Every numerical implementation <math>\mathbf{y}_{n}</math> of a Local Linear discretization <math>\mathbf{z}_{n}</math> is generically called ''Local Linearization scheme''.
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