Symbolic analysis of second-order ordinary differential equations with polynomial coefficients
arXiv:2010.01563 · doi:10.47000/tjmcs.1025121
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 -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.
arXiv comment16 pages, 2 figures. Matches the published version. The codes, a sample worksheet, and the user manual can be obtained from https://github.com/tbirkandan/symODE2
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