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

  • Type:

    Article

  • Date:

    31 December 2014

  • Publication Status:

    Published

  • Publisher

    HIkari

  • DOI:

    10.12988/nade.2014.4712

  • ISSN:

    1314-7587

  • Library of Congress:

    QA Mathematics

  • Dewey Decimal Classification:

    510 Mathematics

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

Authors

Keywords

Ordinary differential equations; general order; series solutions; Fuchs; Frobenius; complex integrals;

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