论文标题
具有多项式系数的二阶普通微分方程的符号分析
Symbolic analysis of second-order ordinary differential equations with polynomial coefficients
论文作者
论文摘要
具有多项式系数的二阶普通微分方程的奇异性结构通常会产生溶液的类型。结果表明，$θ$ - 操作方法可以用作符号计算方法，以获得指示方程和复发关系。因此，如果方程是合适的，则奇异性结构会导致在特殊功能方面产生解决方案的转换。高几何体和HEUN类型方程主要用于物理应用中。因此，只有这些方程式及其汇合类型才与SageMath例程一起考虑在开源软件包Symode2中组装。
The singularity structure of a second-order ordinary differential equation with polynomial coefficients often yields the type of solution. It is shown that the $θ$-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.
