Local linearization method: Difference between revisions

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=== Local Linearization schemes ===

[[File:FigureRDE1.png|thumb|450x400px391x391px|'''Fig. 3''' Phase portrait of trajectories of the ''Euler'' and ''LL'' schemes in the integration of the nonlinear RDE (6.2)-(6.3) with step size ''h=1/32'', and ''p=q=6''.]]

Depending of the approximations <math>\widetilde{\mathbf{\xi }}</math> to the process <math>\mathbf{\xi }</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 the Local Linear discretization <math>\mathbf{z}_{n}</math> is generically called ''Local Linearization scheme.''