- Turkish Journal of Mathematics and Computer Science
- Vol: 14 Issue: 2
- Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients
Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients
Authors : Tolga BİRKANDAN
Pages : 281-291
Doi:10.47000/tjmcs.1025121
View : 7 | Download : 3
Publication Date : 2022-12-30
Article Type : Research
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