On the Convergence of Formal Exotic Series Solutions of an ODE

被引：0

作者：

Gontsov, R. R. ^{[1
,2
]}

Goryuchkina, I., V ^{[3
]}

机构：

[1] RAS, Inst Informat Transmiss Problems, Bolshoy Karetny Per 19,Build 1, Moscow 127051, Russia

[2] Moscow Power Engn Inst, Krasnokazarmennaya 14, Moscow 111250, Russia

[3] RAS, Keldysh Inst Appl Math, Miusskaya Sq 4, Moscow 125047, Russia

来源：

COMPUTATIONAL METHODS AND FUNCTION THEORY | 2020年 / 20卷 / 02期

关键词：

Analytic ODE; Formal solution; Convergent series; Implicit mapping theorem; EXPANSIONS;

D O I：

10.1007/s40315-020-00306-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a sufficient condition for the convergence of a complex power type formal series of the form. = 8 k=1 ak (xi.) xk, where ak are functions meromorphic at the origin and.. R \ {0}, that satisfies an analytic ordinary differential equation (ODE) of a general type. An example of such a type formal solutions of the third Painleve equation is presented and the proposed sufficient condition is applied to check their convergence; moreover, the accumulation of movable poles of these solutions near the critical point is discussed.

引用

页码：279 / 295

页数：17

共 50 条

[1] On the Convergence of Formal Exotic Series Solutions of an ODE
R. R. Gontsov
I. V. Goryuchkina
[J]. Computational Methods and Function Theory, 2020, 20 : 279 - 295
[2] An Analytic Proof of the Malgrange Theorem on the Convergence of Formal Solutions of an ODE
Renat Gontsov
Irina Goryuchkina
[J]. Journal of Dynamical and Control Systems, 2016, 22 : 91 - 100
[3] An Analytic Proof of the Malgrange Theorem on the Convergence of Formal Solutions of an ODE
Gontsov, Renat
Goryuchkina, Irina
[J]. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2016, 22 (01) : 91 - 100
[4] Convergence of a Formal Solution to an ODE
Goryuchkina, Irina V.
[J]. PAINLEVE EQUATIONS AND RELATED TOPICS (2012), 2012, : 23 - 26
[5] An algorithm of multisummation of formal power series, solutions of linear ODE equations
Jung, F
Naegele, F
Thomann, J
[J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 1996, 42 (4-6) : 409 - 425
[6] A Note on the Convergence of Multivariate Formal Power Series Solutions of Meromorphic Pfaffian Systems
Gontsov, Renat
Goryuchkina, Irina
[J]. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2020, 26 (01) : 149 - 158
[7] A Note on the Convergence of Multivariate Formal Power Series Solutions of Meromorphic Pfaffian Systems
Renat Gontsov
Irina Goryuchkina
[J]. Journal of Dynamical and Control Systems, 2020, 26 : 149 - 158
[8] Recent progress in the theory of formal solutions for ODE and PDE
Balser, W
Kostov, V
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2003, 141 (01) : 113 - 123
[9] On convergence sets of formal power series
Ma D.
Neelon T.S.
[J]. Complex Analysis and its Synergies, 1 (1)
[10] On the convergence of generalized power series satisfying an algebraic ODE
Gontsov, R. R.
Goryuchkina, I. V.
[J]. ASYMPTOTIC ANALYSIS, 2015, 93 (04) : 311 - 325

← 1 2 3 4 5 →