On solving boundary value problems for multi-scale systems using asymptotic approximations and multiple-shooting
The authors describe a method for obtaining a numerical solution of singularly perturbed boundary value problems for linear systems of ODE's whose solutions involve dynamics with multiple time scales. A technique to decouple different time scales using a Riccati transformation is presented. For the slow modes, regular perturbation expansion and multiple shooting strategies are combined to apply the technique of the first author and \textit{G. W. M. Staarink} [SIAM J. Sci. Stat. Comput. 5, 745-763 (1984; reviewed above)]. Fast modes, which are assumed to be significant only in endpoint layers, are computed after appropriate stretchings. Some numerical examples are given.
scientific article; zbMATH DE number 3890648
scientific article