TY  - JOUR
TI  - Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients
AB  - 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.
AU  - Birkandan, Tolga
DO  - 10.47000/tjmcs.1025121
PY  - 2022
JO  - Turkish Journal of Mathematics and Computer Science
VL  - 14
IS  - 2
SN  - 2148-1830
SP  - 281
EP  - 291
DB  - TRDizin
UR  - http://search/yayin/detay/1148710
ER  -