Series solutions of partial differential equations using the complex integral method

Robin, William

Abstract

The complex integral method for solving ordinary differential equations in series [3, 7, 8] is extended to cover the series solution of partial differential equations also. The means of this extension is straightforward, with both ‘ordinary’ and ‘Frobenius’ multiple variable power series being dealt with. Standard examples of the application of the extended method(s) to first-order, second-order, third-order and simultaneous partial differential equations are provided throughout. Examples also include the series solution of a non-linear partial differential equation and the consideration of series solutions with negative powers.

Citation

Robin, W. (2014). Series solutions of partial differential equations using the complex integral method. International Mathematical Forum, 9, 1477-1494. https://doi.org/10.12988/imf.2014.48145

• Journal Article Type: Article
• Publication Date: 2014
• Deposit Date: Nov 24, 2014
• Publicly Available Date: Dec 31, 2014
• Publisher: Hikari
• Peer Reviewed: Peer Reviewed
• Volume: 9
• Pages: 1477-1494
• DOI: https://doi.org/10.12988/imf.2014.48145
• Keywords: Partial differential equations; several complex variables; series solutions; complex integrals
• Public URL: http://researchrepository.napier.ac.uk/id/eprint/7314
• Publisher URL: http://dx.doi.org/10.12988/imf.2014.48145