2017/11/08 by E. E. Bukzhalev, Bukzhalev, Evgeny E., А. V. Ovchinnikov +1
Engineering · Mathematics · #34E15 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Material Science and Thermodynamics
paper · pdf · doi:10.48550/arxiv.1711.08050
openalex publication_date 2017/11/08 · openalex created_date 2017/12/04 · openalex updated_date 2026/07/28
We construct a sequence that converges to a solution of the Cauchy problem for a singularly perturbed linear inhomogeneous differential equation of an arbitrary order. This sequence is also an asymptotic sequence in the following sense: the deviation (in the norm of the space of continuous functions) of its nth element from the solution of the problem is proportional to the (n+1)th power of the parameter of perturbation. This sequence can be used for justification of asymptotics obtained by the method of boundary functions.