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

Authors : Tolga BİRKANDAN

Pages : 281-291

Doi:10.47000/tjmcs.1025121

View : 18 | Download : 12

Publication Date : 2022-12-30

Article Type : Research Paper

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