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Using Abel\u27s Theorem to Explain Repeated Roots of the Characteristic Equation [PDF]

, 2011
This document describes how one can derive the solutions to a linear constant coefficient homogeneous differential equation with repeated roots in the characteristic equation with Abel\u27s ...
Green, William
core   +3 more sources

On Solution Representation of Generalized Abel Integral Equation

Journal of Mathematics, 2013
An explicit representation for solution of the generalized Abel integral equation , where is the Riemann-Liouville fractional integral, in terms of the Wright function, is constructed.
Arsen Pskhu
doaj   +1 more source

On the Abel Equation of the Second Kind with Sinusoidal Forcing

Nonlinear Analysis, 2007
We consider the Abel equation of the second kind with sinusoidal forcing, which is a model equation for western boundary outflow in the Stommel model of the large scale ocean circulation.
G. Alobaidi, R. Mallier
doaj   +1 more source

Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials

, 2009
A geometric approach is used to study a family of higher-order nonlinear Abel equations. The inverse problem of the Lagrangian dynamics is studied in the particular case of the second-order Abel equation and the existence of two alternative Lagrangian ...
Abraham R, Boyko V M, Boyko V M, Briskin M, Cariñena J F, Crampin M, Crampin M, Damianou P A, Darboux G, Darboux G, Darboux G, Davis H T, Erbe L, Fernandes R L, Francoise J P, Grundland A M, José F Cariñena, Lopuszanski J, López C, Manuel F Rañada, Murphy G M, Nucci M C, Partha Guha, Polyanin A D, Sarlet W, Sarlet W, Zwillinger D   +26 more
core   +1 more source

Exact solution of the Susceptible–Exposed–Infectious–Recovered–Deceased (SEIRD) epidemic model

Electronic Journal of Qualitative Theory of Differential Equations
An exact solution of an initial value problem for the Susceptible–Exposed–Infectious–Recovered–Deceased (SEIRD) epidemic model is derived, and various properties of the exact solution are obtained.
Norio Yoshida
doaj   +1 more source

U(1)-invariant membranes: the geometric formulation, Abel and pendulum differential equations

, 2010
The geometric approach to study the dynamics of U(1)-invariant membranes is developed. The approach reveals an important role of the Abel nonlinear differential equation of the first type with variable coefficients depending on time and one of the ...
A. A. Zheltukhin, Desgupta A., Desgupta A., Duff M. J., Eisenhart L. P., M. Trzetrzelewski, Saaty T. L., Semenov-Tian-Shanskii M. A., Townsend P. K., Zheltukhin A. A., Zheltukhin A. A., Zheltukhin A. A.   +11 more
core   +1 more source

Material Selection and Geometric Design for Few‐filament Shape Memory Polymer Yarns for Force Generation

Advanced Materials Technologies, EarlyView.
A custom shape memory polymer material selection process relates quantitative application criteria (e.g., compression garment yarns) to material characterization information. The selected materials are manufactured into yarn geometries, which expand the design space by creating structural stress‐strain profiles beyond the nominal material stress‐strain
Michaela Andrews, Susan Mantell, Julianna Abel   +2 more
wiley   +1 more source

Properties of inversion operator of the Abel matrix equation

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2010
Generalization of integral-differential Riemann-Liouville operator on the matrix order-is reviewed and its properties are studied. Theorem of the composition of operators of the matrix of integration and differentiation can be proved.
Rina R Ismagilova
doaj   +3 more sources

Polynomial Solutions of Equivariant Polynomial Abel Differential Equations

Advanced Nonlinear Studies, 2018
Let a⁢(x){a(x)} be non-constant and let bj⁢(x){b_{j}(x)}, for j=0,1,2,3{j=0,1,2,3}, be real or complex polynomials in the variable x. Then the real or complex equivariant polynomial Abel differential equation a⁢(x)⁢y˙=b1⁢(x)⁢y+b3⁢(x)⁢y3{a(x)\dot{y}=b_{1}(
Llibre Jaume, Valls Clàudia
doaj   +1 more source

Universal centers in the cubic trigonometric Abel equation

Electronic Journal of Qualitative Theory of Differential Equations, 2014
We study the center problem for the trigonometric Abel equation $d \rho/ d \theta= a_1 (\theta) \rho^2 + a_2(\theta) \rho^3,$ where $a_1(\theta)$ and $a_2(\theta)$ are cubic trigonometric polynomials in $\theta$.
Jaume Giné, Maite Grau, Xavier Santallusia   +2 more
doaj   +1 more source