Frobenius Series Solution of Fuchs Second-Order 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 Frobenius series solutions for second-order linear homogeneous ordinary Fuchs differential equations. 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 is straightforward to apply as an algorithm, and eliminates the manipulation of power series, so characteristic of the usual approach [14]. The method is a generalization of a procedure developed by Herrera [4] for finding Maclaurin series solutions for nonlinear differential equations.

Citation

Robin, W. (2014). Frobenius Series Solution of Fuchs Second-Order Ordinary Differential Equations via Complex Integration. International Mathematical Forum, 9, 953-965. https://doi.org/10.12988/imf.2014.4491

• Journal Article Type: Article
• Publication Date: 2014
• Deposit Date: Apr 15, 2015
• Publicly Available Date: Apr 15, 2015
• Electronic ISSN: 1312-7594
• Publisher: Hikari
• Peer Reviewed: Peer Reviewed
• Volume: 9
• Pages: 953-965
• DOI: https://doi.org/10.12988/imf.2014.4491
• Keywords: Frobenius; Series solution; Fuchs differential equations; complex integrals
• Public URL: http://researchrepository.napier.ac.uk/id/eprint/7764
• Publisher URL: http://dx.doi.org/10.12988/imf.2014.4491