Thus, only these equations and their confluent types are considered with SageMath routines which are assembled in the open-source package symODE2.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:The singularity structure of a second-order ordinary differential equation with polynomial coefficients often yields the type of solution.
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Temel Bulgular & Veri:Consequently, the singularity structure leads to the transformations that yield a solution in terms of a special function, if the equation is suitable.
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Sonuç & Katkı:Thus, only these equations and their confluent types are considered with SageMath routines which are assembled in the open-source package symODE2.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Ordinary differential equations · symbolic analysis · special functions
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.
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