On the construction of solutions of systems of linear ordinary differential equations in the neighbourhood of a regular singularity

V. I. Galiev; A. F. Polupanov; I. E. Shparlinski

doi:10.1016/0377-0427(92)90126-I

On the construction of solutions of systems of linear ordinary differential equations in the neighbourhood of a regular singularity

V. I. Galiev^*, A. F. Polupanov, I. E. Shparlinski

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

A method allowing to construct successively all linearly independent solutions of systems of linear ordinary differential equations in the neighbourhood of a regular singularity as algebraic combinations of a power series, power and a logarithmic function log x is proposed. The solutions are constructed both in the cases of a simple and defect "leading" matrix of coefficients in equations. The convergence of power series in solutions is proven and the estimate of the errors which arise due to the truncation of these series is obtained. An application of the method to solving one-particle Schrödinger equations is discussed.

Original language	English
Pages (from-to)	151-163
Number of pages	13
Journal	Journal of Computational and Applied Mathematics
Volume	39
Issue number	2
DOIs	https://doi.org/10.1016/0377-0427(92)90126-I
Publication status	Published - 30 Mar 1992
Externally published	Yes

Keywords

Ordinary differential equations
regular singularity
Schrödinger equation

Access to Document

10.1016/0377-0427(92)90126-I

Cite this

@article{289921a59a004b56bf43e7eb40eb372a,

title = "On the construction of solutions of systems of linear ordinary differential equations in the neighbourhood of a regular singularity",

abstract = "A method allowing to construct successively all linearly independent solutions of systems of linear ordinary differential equations in the neighbourhood of a regular singularity as algebraic combinations of a power series, power and a logarithmic function log x is proposed. The solutions are constructed both in the cases of a simple and defect {"}leading{"} matrix of coefficients in equations. The convergence of power series in solutions is proven and the estimate of the errors which arise due to the truncation of these series is obtained. An application of the method to solving one-particle Schr{\"o}dinger equations is discussed.",

keywords = "Ordinary differential equations, regular singularity, Schr{\"o}dinger equation",

author = "Galiev, {V. I.} and Polupanov, {A. F.} and Shparlinski, {I. E.}",

year = "1992",

month = mar,

day = "30",

doi = "10.1016/0377-0427(92)90126-I",

language = "English",

volume = "39",

pages = "151--163",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier",

number = "2",

}

TY - JOUR

T1 - On the construction of solutions of systems of linear ordinary differential equations in the neighbourhood of a regular singularity

AU - Galiev, V. I.

AU - Polupanov, A. F.

AU - Shparlinski, I. E.

PY - 1992/3/30

Y1 - 1992/3/30

N2 - A method allowing to construct successively all linearly independent solutions of systems of linear ordinary differential equations in the neighbourhood of a regular singularity as algebraic combinations of a power series, power and a logarithmic function log x is proposed. The solutions are constructed both in the cases of a simple and defect "leading" matrix of coefficients in equations. The convergence of power series in solutions is proven and the estimate of the errors which arise due to the truncation of these series is obtained. An application of the method to solving one-particle Schrödinger equations is discussed.

AB - A method allowing to construct successively all linearly independent solutions of systems of linear ordinary differential equations in the neighbourhood of a regular singularity as algebraic combinations of a power series, power and a logarithmic function log x is proposed. The solutions are constructed both in the cases of a simple and defect "leading" matrix of coefficients in equations. The convergence of power series in solutions is proven and the estimate of the errors which arise due to the truncation of these series is obtained. An application of the method to solving one-particle Schrödinger equations is discussed.

KW - Ordinary differential equations

KW - regular singularity

KW - Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=0039956561&partnerID=8YFLogxK

U2 - 10.1016/0377-0427(92)90126-I

DO - 10.1016/0377-0427(92)90126-I

M3 - Article

AN - SCOPUS:0039956561

SN - 0377-0427

VL - 39

SP - 151

EP - 163

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

On the construction of solutions of systems of linear ordinary differential equations in the neighbourhood of a regular singularity

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this