scholarly journals Rational Solutions of High-Order Algebraic Ordinary Differential Equations

2019 ◽  
Vol 33 (3) ◽  
pp. 821-835
Author(s):  
Thieu N. Vo ◽  
Yi Zhang
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
High Order ◽  
Rational Solutions ◽  
Order Algebraic

scholarly journals On Conjugacy of High-Order Linear Ordinary Differential Equations

1994 ◽  
Vol 1 (1) ◽  
pp. 1-8
Author(s):  
T. Chanturia
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
High Order ◽  
Summable Function ◽  
Order Linear ◽  
Linear Ordinary Differential Equations

Abstract It is shown that the differential equation u (n) = p(t)u, where n ≥ 2 and p : [a, b] → ℝ is a summable function, is not conjugate in the segment [a, b], if for some l ∈ {1, . . . , n – 1}, α ∈]a, b[ and β ∈]α, b[ the inequalities hold.

scholarly journals On a class of linear ordinary differential equations having∑k=0∞xkδ(k)(t)and∑k=0mxkδ(k)(t)as solutions

1996 ◽  
Vol 19 (3) ◽  
pp. 555-562
Author(s):  
Ahmed D. Alawneh ◽  
Ahmed Y. Farah
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Rational Solution ◽  
Rational Solutions ◽  
Homogeneous Case ◽  
Linear Ordinary Differential Equations ◽  
Partial Sum ◽  
Distributional Solutions ◽  
Finite Solution

We introduced some linear homogeneous ordinary differential equations which have both formal and finite distributional solutions at the same time, where the finite solution is a partial sum of the formal one. In the nonhomogeneous case and sometimes in the homogeneous case we found formal rational and rational solutions for such differential equations and similarly the rational solution is a partial sum of the formal one.

A high-order discontinuous Galerkin approximation to ordinary differential equations with applications to elastodynamics

2017 ◽  
Vol 38 (4) ◽  
pp. 1709-1734 ◽  
Author(s):  
Paola F Antonietti ◽  
Ilario Mazzieri ◽  
Niccolò Dal Santo ◽  
Alfio Quarteroni
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Discontinuous Galerkin ◽  
Galerkin Approximation ◽  
High Order
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