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A Method to Study the Cauchy Problem for a Singularly Perturbed Homogeneous Linear Differential Equation of Arbitrary Order
Authors:Email author" target="_blank">E?E?BukzhalevEmail author
Institution:1.Moscow State University, Faculty of Physics,Leninskie Gory, Moscow,Russia
Abstract:We construct a sequence converging to the solution to the Cauchy problem for a singularly perturbed linear homogeneous differential equation of any order. This sequence is asymptotic in the following sense: the distance (with respect to the norm of the space of continuous functions) between its nth element and the solution to the problem is proportional to the (n + 1)th power of the perturbation parameter.
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