Asymptotic solution of a singularly perturbed Cauchy problem with a turning point
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 156 (2018), pp. 84-88.

Voir la notice de l'article provenant de la source Math-Net.Ru

Using a modified method of boundary-layer functions, we construct a complete uniform asymptotic solution to the singularly perturbed Cauchy problem for a second-order linear inhomogeneous ordinary differential equation with a multiple turning point on the real axis.
Keywords: asymptotics, boundary-layer function, Cauchy problem, bisingular problem, turning point, generalized method of boundary-layer functions, singular perturbation.
@article{INTO_2018_156_a6,
     author = {D. A. Tursunov and K. G. Kozhobekov},
     title = {Asymptotic solution of a singularly perturbed {Cauchy} problem with a turning point},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {84--88},
     publisher = {mathdoc},
     volume = {156},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_156_a6/}
}
TY  - JOUR
AU  - D. A. Tursunov
AU  - K. G. Kozhobekov
TI  - Asymptotic solution of a singularly perturbed Cauchy problem with a turning point
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2018
SP  - 84
EP  - 88
VL  - 156
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2018_156_a6/
LA  - ru
ID  - INTO_2018_156_a6
ER  - 
%0 Journal Article
%A D. A. Tursunov
%A K. G. Kozhobekov
%T Asymptotic solution of a singularly perturbed Cauchy problem with a turning point
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2018
%P 84-88
%V 156
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2018_156_a6/
%G ru
%F INTO_2018_156_a6
D. A. Tursunov; K. G. Kozhobekov. Asymptotic solution of a singularly perturbed Cauchy problem with a turning point. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 156 (2018), pp. 84-88. http://geodesic.mathdoc.fr/item/INTO_2018_156_a6/

[1] \label{D1} Alymkulov K., Tursunov D. A., “Ob odnom metode postroeniya asimptoticheskikh razlozhenii reshenii bisingulyarno vozmuschennykh zadach”, Izv. vuzov. Mat., 2016, no. 12, 3–11 | Zbl

[2] Zaitsev V. F., Polyanin A. D., Spravochnik po obyknovennym differentsialnym uravneniyam, Fizmatlit, M., 2001 | MR

[3] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraveykh zadach, Nauka, M., 1989

[4] Lomov S. A., Vvedenie v obschuyu teoriyu singulyarnykh vozmuschenii, Nauka, M., 1981

[5] \label{D2} Tursunov D. A., “Asimptoticheskoe razlozhenie resheniya obyknovennogo differentsialnogo uravneniya vtorogo poryadka s tremya tochkami povorota”, Tr. IMM UrO RAN, 22:1 (2016), 271–281 | MR

[6] \label{D3} Tursunov D. A., “Asimptoticheskoe razlozhenie resheniya singulyarno vozmuschennogo obyknovennogo differentsialnogo uravneniya vtorogo poryadka s dvumya tochkami povorota”, Vestn. Tomsk. gos. un-ta. Mat. mekh., 2013, no. 1 (21), 34–40

[7] Tursunov D. A., “Asimptoticheskoe reshenie bisingulyarnoi zadachi Robena”, Sib. elektr. mat. izv., 14 (2017), 10–21 | MR | Zbl

[8] Kevorkian J., Cole J. D., Perturbation methods in applied mathematics, Springer-Verlag, 1968 | MR

[9] Olver F. M., “Connection formulas for second-order differential equations with multiple turning points”, SIAM J. Math. Anal., 1:8 (1977), 127–154 | DOI | MR

[10] Olver F. M., “Connection formulas for second-order differential equations having an arbitrary number of turning points of arbitrary multiplicities”, SIAM J. Math. Anal., 4:8 (1977), 673–700 | DOI | MR

[11] Van Dyke M., Perturbation methods in fluid dynamics, Academic Press, New York, 1964 | MR

[12] Wasow W., Asymptotic expansions for ordinary differential equations, Dover, New York, 1965 | MR

[13] Wasow W., Linear turning point theory, Springer-Verlag, New York, 1985 | MR | Zbl

[14] Watts A. M., “A singular perturbation problem with a turning point”, Bull. Austr. Math. Soc., 5 (1971), 61–73 | DOI | MR | Zbl

[15] Wong R., Selected papers of F. W. J. Olver, World Scientific, 2000 | MR | Zbl