Series Solution of Second-Order Linear Homogeneous Ordinary Differential Equations via Complex Integration

Robin, William

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: Apr 16, 2015
• 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