Method of finite elements for solving singular ordinary differential equation of 4-th order without special forms for boundary layers

10.12737/6770 ◽  
2014 ◽  
Vol 2 (5) ◽  
pp. 134-137
Author(s):  
A. Al-Imam ◽  
S. Noaman ◽  
N. Verveyko
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Finite Elements ◽  
Boundary Layers ◽  
Method Of Finite Elements ◽  
Singular Ordinary Differential Equation

Integrable-square solutions of a singular ordinary differential equation

1981 ◽  
Vol 89 (3-4) ◽  
pp. 267-279 ◽  
Author(s):  
Richard C. Gilbert
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Characteristic Polynomial ◽  
Characteristic Equation ◽  
Complex Plane ◽  
Asymptotic Expansions ◽  
Differential Operators ◽  
Singular Ordinary Differential Equation ◽  
Ordinary Differential Operators

SynopsisAbsolutely square integrable solutions are determined for the equation= λywhere the ζn−r(x) are holomorphic in a sector of the complex plane and have asymptotic expansions asxapproaches infinity. It is shown that the number of such solutions depends upon the roots of the characteristic equation and their multiplicity, and upon the sign of the derivative of the characteristic polynomial. Application is made to formally symmetric ordinary differential operators.

The Reduction of a Type of Singular Partial Differential Equations

2014 ◽  
Vol 602-605 ◽  
pp. 3616-3619
Author(s):  
Ping Li Li ◽  
Tian Tian Sun
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Complex Domain ◽  
Partial Differential ◽  
Singular Ordinary Differential Equation

Using the theory with respect to the existence of holomorphic solutions to a singular ordinary differential equation in the complex domain, this paper shows how to constructs biholomorphic trans-formations in different cases to reduce partial differential equations with singularity at the origin to more simple forms.

scholarly journals Multiple positive solutions to mixed boundary value problems for singular ordinary differential equations on the whole line

2012 ◽  
Vol 17 (4) ◽  
pp. 460-480 ◽  
Author(s):  
Yuji Yuji
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Nonnegative Function ◽  
Multiple Positive Solutions ◽  
Mixed Boundary Value Problem ◽  
One Dimensional ◽  
Singular Ordinary Differential Equation ◽  
The One

This paper is concerned with the mixed boundary value problem of the second order singular ordinary differential equation[Φ(ρ(t)x'(t))]' + f(t, x(t), x'(t)) = 0,   t ∈ R,limt→−∞ x(t) = ∫−∞+∞ g(s, x(s), x'(s)) ds,limt→+∞ ρ(t)x'(t) =  ∫−∞+∞h(s, x(s), x' (s)) ds.Sufficient conditions to guarantee the existence of at least one positive solution are established. The emphasis is put on the one-dimensional p-Laplacian term [Φ(ρ(t)x'(t))]' involved with the nonnegative function ρ satisfying ∫−∞+∞1/ρ(s) ds = +∞.

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