Abstract
In this paper, we apply the singular renormalization group (RG) method to study the initial value problem of slow‐fast system. Based on some basic assumptions, we construct a uniformly valid approximate solution by an explicit renormalization group procedure, and then give a rigorous proof of the error estimate up to second order. Moreover, a classical example in optimal control is presented to illustrate the effectiveness. Our results extend the applications of RG method to some extent and are consistent with previous results as well.
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