On the procedure for the series solution of second-order homogeneous linear differential equation via the complex integration method

Robin, W.

Abstract

The theory of series solutions for second-order linear homogeneous ordinary differential equation is developed ab initio, using an elementary complex integral expression (based on Herrera’ work [3]) derived and applied in previous papers [8, 9]. As well as reproducing the usual expression for the recurrence relations for second-order equations, the general solution method is straight-forward to apply as an algorithm on its own, with the integral algorithm replacing the manipulation of power series by reducing the task of finding a series solution for second-order equations to the solution, instead, of a system of uncoupled simple equations in a single unknown. The integral algorithm also simplifies the construction of ‘logarithmic solutions’ to second-order Fuchs, equations. Examples, from the general science and mathematics literature, are presented throughout.

Citation

Robin, W. (2014). On the procedure for the series solution of second-order homogeneous linear differential equation via the complex integration method. Nonlinear Analysis and Differential Equations, 2(4), 173-188. https://doi.org/10.12988/nade.2014.4713

• Journal Article Type: Article
• Acceptance Date: Jun 1, 2014
• Publication Date: 2014
• Deposit Date: Apr 14, 2015
• Publicly Available Date: Apr 14, 2015
• Journal: Nonlinear Analysis and Differential Equations
• Print ISSN: 1314-7587
• Peer Reviewed: Peer Reviewed
• Volume: 2
• Issue: 4
• Pages: 173-188
• DOI: https://doi.org/10.12988/nade.2014.4713
• Keywords: Frobenius; series solution; Fuchs differential equations; complex Integrals
• Public URL: http://researchrepository.napier.ac.uk/id/eprint/7759
• Publisher URL: http://dx.doi.org/10.12988/nade.2014.4713
• Contract Date: Apr 14, 2015