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

Birkandan, Tolga

doi:10.47000/tjmcs.1025121

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

Tolga BİRKANDAN (İstanbul Teknik Üniversitesi, Fizik Bölümü, İstanbul, Türkiye)

Turkish Journal of Mathematics and Computer Science

3 2

Yıl: 2022 Cilt: 14 Sayı: 2 Sayfa Aralığı: 281 - 291 Metin Dili: İngilizce DOI: 10.47000/tjmcs.1025121 İndeks Tarihi: 17-01-2023

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

Öz:

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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APA	Birkandan T (2022). Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients. , 281 - 291. 10.47000/tjmcs.1025121
Chicago	Birkandan Tolga Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients. (2022): 281 - 291. 10.47000/tjmcs.1025121
MLA	Birkandan Tolga Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients. , 2022, ss.281 - 291. 10.47000/tjmcs.1025121
AMA	Birkandan T Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients. . 2022; 281 - 291. 10.47000/tjmcs.1025121
Vancouver	Birkandan T Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients. . 2022; 281 - 291. 10.47000/tjmcs.1025121
IEEE	Birkandan T "Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients." , ss.281 - 291, 2022. 10.47000/tjmcs.1025121
ISNAD	Birkandan, Tolga. "Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients". (2022), 281-291. https://doi.org/10.47000/tjmcs.1025121

APA	Birkandan T (2022). Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients. Turkish Journal of Mathematics and Computer Science, 14(2), 281 - 291. 10.47000/tjmcs.1025121
Chicago	Birkandan Tolga Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients. Turkish Journal of Mathematics and Computer Science 14, no.2 (2022): 281 - 291. 10.47000/tjmcs.1025121
MLA	Birkandan Tolga Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients. Turkish Journal of Mathematics and Computer Science, vol.14, no.2, 2022, ss.281 - 291. 10.47000/tjmcs.1025121
AMA	Birkandan T Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients. Turkish Journal of Mathematics and Computer Science. 2022; 14(2): 281 - 291. 10.47000/tjmcs.1025121
Vancouver	Birkandan T Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients. Turkish Journal of Mathematics and Computer Science. 2022; 14(2): 281 - 291. 10.47000/tjmcs.1025121
IEEE	Birkandan T "Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients." Turkish Journal of Mathematics and Computer Science, 14, ss.281 - 291, 2022. 10.47000/tjmcs.1025121
ISNAD	Birkandan, Tolga. "Symbolic Analysis of Second-order Ordinary Differential Equations with Polynomial Coefficients". Turkish Journal of Mathematics and Computer Science 14/2 (2022), 281-291. https://doi.org/10.47000/tjmcs.1025121