Geodesic
The asymptotic decomposition of solution of singularly perturbed differential and operational equation in the critical case
Matematičeskoe modelirovanie, Tome 26 (2014) no. 4, pp. 65-79

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Formal asymptotic decomposition on small parameter of solution for initial task for singularly perturbed differential and operator equation in critical case is constructed. Estimates of functions of splash and boundary functions are found, assessment of residual member of decomposition is received.
Keywords: asymptotic decomposition of solution, small parameter, singularly perturbations, differential and operator equations, initial task, critical case, modified method of boundary functions. 
@article{MM_2014_26_4_a5,
     author = {A. V. Zaborskiy and A. V. Nesterov},
     title = {The asymptotic decomposition of solution of singularly perturbed differential and operational equation in the critical case},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {65--79},
     publisher = {mathdoc},
     volume = {26},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2014_26_4_a5/}
}
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A. V. Zaborskiy; A. V. Nesterov. The asymptotic decomposition of solution of singularly perturbed differential and operational equation in the critical case. Matematičeskoe modelirovanie, Tome 26 (2014) no. 4, pp. 65-79. http://geodesic.mathdoc.fr/item/MM_2014_26_4_a5/