Improvement of Perturbation Series
The principal shortcoming of perturbation methods is the local nature of solutions based on them. Besides that, the following questions are very difficult for the theory: what values mayε be considered as small (large)? How can a solution for may ε be constructed if its behaviour is known for ε → 0 and ε → ∞? As the technique of asymptotic integration is well developed and widely used, such problems as elimination of the locality of expansion, evaluation of the convergence domain, construction of uniformly suitable solutions are very urgent.
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