On Existence and Uniqueness of Formal Power Series Solutions of Algebraic Ordinary Differential Equations

被引：0

作者：

Sebastian Falkensteiner

Yi Zhang

Thieu N. Vo

机构：

[1] Johannes Kepler University,Research Institute for Symbolic Computation (RISC)

[2] Xi’an Jiaotong-Liverpool University,Department of Applied Mathematics, School of Science

[3] Ton Duc Thang University,Fractional Calculus, Optimization and Algebra Research Group, Faculty of Mathematics and Statistics

来源：

Mediterranean Journal of Mathematics | 2022年 / 19卷

关键词：

Formal power series; algebraic differential equation; 34A05; 34A09; 68W30;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Given an algebraic ordinary differential equation (AODE), we propose a computational method to determine when a truncated power series can be extended to a formal power series solution. If a certain regularity condition on the given AODE or on the initial values is fulfilled, we compute all of the solutions. Moreover, when the existence is confirmed, we present the algebraic structure of the set of all formal power series solutions.

引用

共 50 条

[1] On Existence and Uniqueness of Formal Power Series Solutions of Algebraic Ordinary Differential Equations
Falkensteiner, Sebastian
Zhang, Yi
Vo, Thieu N.
[J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2022, 19 (02)
[2] EXISTENCE AND UNIQUENESS OF SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS
WEND, DVV
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 23 (01) : 27 - &
[3] Existence and uniqueness theorems for formal power series solutions of analytic differential systems
Rust, CJ
Reid, GJ
Wittkopf, AD
[J]. ISSAC 99: PROCEEDINGS OF THE 1999 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, 1999, : 105 - 112
[4] ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS OF NONLINEAR SEMIIMPLICIT DIFFERENTIAL ALGEBRAIC EQUATIONS
RHEINBOLDT, WC
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1991, 16 (7-8) : 647 - 661
[5] FORMAL POWER SERIES AS INTEGRALS OF ALGEBRAIC DIFFERENTIAL EQUATIONS
MAHLER, K
[J]. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI RENDICONTI-CLASSE DI SCIENZE FISICHE-MATEMATICHE & NATURALI, 1971, 50 (02): : 76 - &
[6] POWER SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS
DETTMAN, JW
[J]. AMERICAN MATHEMATICAL MONTHLY, 1967, 74 (04): : 428 - &
[7] Special formal series solutions of linear ordinary differential equations
Ryabenko, A
[J]. FORMAL POWER SERIES AND ALGEBRAIC COMBINATORICS, 2000, : 356 - 366
[8] Existence and uniqueness of optimal solutions for multirate partial differential algebraic equations
Kugelmann, Bernd
Pulch, Roland
[J]. APPLIED NUMERICAL MATHEMATICS, 2015, 97 : 69 - 87
[9] EXISTENCE AND UNIQUENESS RESULTS FOR ORDINARY DIFFERENTIAL EQUATIONS
Aslanov, Afgan
[J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2009, 39 (06) : 1809 - 1835
[10] UNIQUENESS OF SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS
WEND, DVV
[J]. AMERICAN MATHEMATICAL MONTHLY, 1967, 74 (08): : 948 - &

← 1 2 3 4 5 →