scholarly journals Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula

2007 ◽  
Vol 5 (2) ◽  
pp. 415-427 ◽  
Author(s):  
Hans J. Weber
Keyword(s):  
Differential Equations ◽  
Real Polynomial ◽  
Rodrigues Formula ◽  
Polynomial Solutions ◽  
Hypergeometric Type

scholarly journals On a Symmetric Generalization of Bivariate Sturm–Liouville Problems

2021 ◽  
Author(s):  
Yves Guemo Tefo ◽  
Rabia Aktaş ◽  
Iván Area ◽  
Esra Güldoğan Lekesiz
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Orthogonal Polynomial ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Polynomial Solutions ◽  
New Class ◽  
Polynomial Coefficients ◽  
Sturm Liouville ◽  
Hypergeometric Type

AbstractA new class of partial differential equations having symmetric orthogonal solutions is presented. The general equation is presented and orthogonality is obtained using the Sturm–Liouville approach. Conditions on the polynomial coefficients to have admissible partial differential equations are given. The general case is analyzed in detail, providing orthogonality weight function, three-term recurrence relations for the monic orthogonal polynomial solutions, as well as explicit form of these monic orthogonal polynomial solutions, which are solutions of an admissible and potentially self-adjoint linear second-order partial differential equation of hypergeometric type.

Analytic approximate solutions for a class of variable order fractional differential equations using the polynomial least squares method

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Constantin Bota ◽  
Bogdan Căruntu
Keyword(s):  
Differential Equations ◽  
Least Squares ◽  
Fractional Differential Equations ◽  
Least Squares Method ◽  
Approximate Solutions ◽  
Variable Order ◽  
Polynomial Solutions ◽  
Fractional Differential ◽  
Approximate Polynomial

AbstractIn this paper a new way to compute analytic approximate polynomial solutions for a class of nonlinear variable order fractional differential equations is proposed, based on the Polynomial Least Squares Method (PLSM). In order to emphasize the accuracy and the efficiency of the method several examples are included.

On the polynomial solutions of ordinary differential equations of the fourth order

1985 ◽  
Vol 26 (7) ◽  
pp. 1547-1552 ◽  
Author(s):  
J. S. Dehesa ◽  
E. Buendia ◽  
M. A. Sanchez‐Buendia
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Polynomial Solutions
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