William Robin
Series Solution of Second-Order Linear Homogeneous Ordinary Differential Equations via Complex Integration
Robin, William
Authors
Abstract
A method is presented, with standard examples, based on an elementary complex integral expression, for developing, in particular, series solutions for second-order linear homogeneous ordinary differential equations. Straightforward to apply, the method reduces the task of finding a series solution to the solution, instead, of a system of simple equations in a single variable. The method eliminates the need to manipulate power series and balance powers, which is a characteristic of the usual approach. The method originated with Herrera [3], but was applied to the solution of certain classes of nonlinear ordinary differential equations by him.
Citation
Robin, W. (2014). Series Solution of Second-Order Linear Homogeneous Ordinary Differential Equations via Complex Integration. International Mathematical Forum, 9, 967-976. https://doi.org/10.12988/imf.2014.4492
Journal Article Type | Article |
---|---|
Publication Date | 2014 |
Deposit Date | Apr 16, 2015 |
Publicly Available Date | Mar 29, 2024 |
Electronic ISSN | 1312-7594 |
Publisher | Hikari |
Peer Reviewed | Peer Reviewed |
Volume | 9 |
Pages | 967-976 |
DOI | https://doi.org/10.12988/imf.2014.4492 |
Keywords | Series solution, ordinary differential equations, complex integrals |
Public URL | http://researchrepository.napier.ac.uk/id/eprint/7765 |
Publisher URL | http://dx.doi.org/10.12988/imf.2014.4492 |
Files
Robin_Series_Solution_of_Second-Order_Linear_Homogeneous_Ordinary_Differential_Equations_via_Complex_Integration.pdf
(126 Kb)
PDF
Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/
Copyright Statement
This article is distributed under the Creative Commons Attribution License.
You might also like
Iterative solutions to classical second-order ordinary differential equations
(2019)
Journal Article
On compact uniform analytical approximations to the Blasius Velocity profile.
(2015)
Journal Article
Some new uniform approximate analytical representations of the Blasius function.
(2015)
Journal Article
Ladder-Operator Factorization and the Bessel Differential Equations
(2014)
Journal Article
Downloadable Citations
About Edinburgh Napier Research Repository
Administrator e-mail: repository@napier.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search