TY - JOUR
T1 - On Existence and Uniqueness of Formal Power Series Solutions of Algebraic Ordinary Differential Equations
AU - Falkensteiner, Sebastian
AU - Zhang, Yi
AU - Vo, Thieu N.
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2022/4
Y1 - 2022/4
N2 - 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.
AB - 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.
KW - Formal power series
KW - algebraic differential equation
UR - http://www.scopus.com/inward/record.url?scp=85125464957&partnerID=8YFLogxK
U2 - 10.1007/s00009-022-01984-w
DO - 10.1007/s00009-022-01984-w
M3 - Article
AN - SCOPUS:85125464957
SN - 1660-5446
VL - 19
JO - Mediterranean Journal of Mathematics
JF - Mediterranean Journal of Mathematics
IS - 2
M1 - 74
ER -