Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients

Year 2022, Volume: 14 Issue: 2, 281 - 291, 30.12.2022

Tolga Birkandan

https://doi.org/10.47000/tjmcs.1025121

Cited By: 2

Abstract

The singularity structure of a second-order ordinary differential equation with polynomial coefficients often yields the type of solution. It is shown that the $\theta$-operator method can be used as a symbolic computational approach to obtain the indicial equation and the recurrence relation. Consequently, the singularity structure leads to the transformations that yield a solution in terms of a special function, if the equation is suitable. Hypergeometric and Heun-type equations are mostly employed in physical applications. Thus, only these equations and their confluent types are considered with SageMath routines which are assembled in the open-source package symODE2.

Keywords

Ordinary differential equations, symbolic analysis, special functions

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