Abstract

This work advances a general framework to obtain the solution of nonlinear ordinary differential equations (ODEs) via power series methods. The approach is demonstrated through problems relevant to mathematical physics. Power series solutions can offer advantages over other numerical techniques in many applications, including increased convergence and computational efficiency. The theoretical basis for power series and their convergence rests in the complex-analytic structure of the function being computed. The existence of convergence-limiting singularities in the complex plane, their location, and their asymptotic behavior motivate analytic continuation techniques to overcome their influence. This work demonstrates some methods to manage singularities, not least by examining asymptotic behaviors of the ODE, thereby providing useful solutions several physical problems. The proposed advancements and their applications improve the utility of power series solutions in both theoretical and practical contexts, paving the way for further research.

Publication Date

5-2026

Document Type

Dissertation

Student Type

Graduate

Degree Name

Mathematical Modeling (Ph.D)

Department, Program, or Center

Mathematics and Statistics, School of

College

College of Science

Advisor

Steven J. Weinstein

Advisor/Committee Member

Nathaniel S. Barlow

Advisor/Committee Member

Michael J Schertzer

Campus

RIT – Main Campus

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