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

  • Type:

    Article

  • Date:

    31 December 2014

  • Publication Status:

    Published

  • Publisher

    HIKARI Ltd

  • DOI:

    10.12988/nade.2014.4713

  • 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 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

Authors

Keywords

Frobenius; series solution; Fuchs differential equations; complex Integrals;

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