On the procedure for the series solution of certain general-order homogeneous linear differential equations via the complex integration method.

Robin, William

Abstract

The theory of series solutions for two important classes of the general higher-order linear homogeneous ordinary differential equation is developed ab initio, using an elementary complex integral expression derived and applied in previous papers [10, 11], based on the original work of Herrera [5]. As well as producing general expressions for the recurrence relations for higher-order equations with analytic coefficients or the general-order Fuchs’ equation, the complex integral method is straight-forward to apply as an algorithm on its own. ‘Benchmark’ examples from the general mathematic literature, are presented and a brief discussion of ‘logarithmic’ solutions is included.

Citation

Robin, W. (2014). On the procedure for the series solution of certain general-order homogeneous linear differential equations via the complex integration method. Nonlinear Analysis and Differential Equations, 2, 155-171. https://doi.org/10.12988/nade.2014.4712

• Journal Article Type: Article
• Publication Date: 2014
• Deposit Date: Sep 16, 2014
• Publicly Available Date: Dec 31, 2014
• Print ISSN: 1314-7587
• Electronic ISSN: 2367-4814
• Peer Reviewed: Not Peer Reviewed
• Volume: 2
• Pages: 155-171
• DOI: https://doi.org/10.12988/nade.2014.4712
• Keywords: Ordinary differential equations; general order; series solutions; Fuchs; Frobenius; complex integrals
• Public URL: http://researchrepository.napier.ac.uk/id/eprint/7157
• Publisher URL: http://dx.doi.org/10.12988/nade.2014.4712