Functions and Analysis

    

The Generating Function Technique and Algebraic Ordinary Differential Equations

Authors: Robert Lloyd Jackson

In the past, theorems have shown that individuals can implement a (formal) power series method to derive solutions to algebraic ordinary differential equations, or AODEs. First, this paper will give a quick synopsis of these “bottom-up” approaches while further elaborating on a recent theorem that established the (modified) generating function technique, or [m]GFT, as a powerful method for solving differentials equations. Instead of building a (formal) power series, the latter method uses a predefined set of (truncated) Laurent series comprised of polynomial linear, exponential, hypergeometric, or hybrid rings to produce an analytic solution. Next, this study will utilize the [m]GFT to create several analytic solutions to a few example AODEs. Ultimately, one will find [m]GFT may serve as a powerful "top-down" method for solving linear and nonlinear AODEs.

Comments: 8 Pages. contact at rljacksonmd@gmail.com

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Submission history

[v1] 2022-05-17 13:35:04
[v2] 2022-05-19 21:58:17
[v3] 2022-06-04 01:51:42
[v4] 2022-06-08 01:20:01

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