Results 71 to 80 of about 36,805 (178)
A connection between Abel and $_p{\rm F}_q$ hypergeometric differential equations
European Journal of Applied Mathematics, 2005 In a recent paper, a new 3-parameter class of Abel type equations, so-called AIR, all of whose members can be mapped into Riccati equations, is shown. Most of the Abel equations with solution presented in the literature belong to the AIR class. Three canonical forms were shown to generate this class, according to the roots of a cubic.
openaire +3 more sources
NUMERICAL STUDIES FOR SOLVING ABEL'S DIFFERENTIAL EQUATION
Malaysian Journal of Industrial TechnologyThis paper uses the Abel's Equation, often used in various fields including physics and engineering, represents a mathematical model that can be complex to solve analytically. This research focuses on solving the Abel's Equation using several numerical methods: Euler's method, Taylor series method, Adomian decomposition method, and Runge-Kutta method ...
null T. F. A. Almajbri. +2 more
openaire +1 more source
From Abel’s differential equations to Hilbert’s 16th problem
São Paulo Journal of Mathematical SciencesAbstractThe study of the limit cycles of planar polynomial differential equations is motivated both by its appearance in many mathematical models of the real-world as for the second part of Hilbert’s 16th problem. In this work we briefly summarize some results on this subject and we will also highlight the important role that the Abel’s differential ...
openaire +3 more sources
Dust Universes in Higher Dimensions with Gauss–Bonnet Corrections
UniverseWe study dust models in higher-dimensional general relativity and the Einstein–Gauss–Bonnet theory in a maximally symmetric spacetime. We show that the dynamics of the model is governed by an Abel differential equation of the second kind.
Sumeekha Singh +2 more
doaj +1 more source
Revolving scheme for solving a cascade of Abel equations in dynamics of planar satellite rotation
Theoretical and Applied Mechanics Letters, 2017 The main objective for this research was the analytical exploration of the dynamics of planar satellite rotation during the motion of an elliptical orbit around a planet. First, we revisit the results of J. Wisdom et al.
Sergey V. Ershkov
doaj +1 more source
Analytical solution of linear ordinary differential equations by differential transfer matrix method
, 2003 We report a new analytical method for exact solution of homogeneous linear ordinary differential equations with arbitrary order and variable coefficients.
Adibi, Ali, Khorasani, Sina
core +2 more sources
Solution of Abel Integral Equation Using Differential Transform Method
JOURNAL OF ADVANCES IN MATHEMATICS, 2018 The application of fractional differential transform method, developed for differential equations of fractional order, are extended to derive exact analytical solutions of fractional order Abel integral equations. The fractional integrations are described in the Riemann-Liouville sense and fractional derivatives are described in the Caputo sense.
Subhabrata Mondal, B. N. Mandal
openaire +2 more sources
Nonlinear Engineering, 2019 Fractional calculus and fractional differential equations (FDE) have many applications in different branches of sciences. But, often a real nonlinear FDE has not the exact or analytical solution and must be solved numerically.
Parand K., Nikarya M.
doaj +1 more source
Constant invariant solutions of the Poincare center-focus problem
Electronic Journal of Differential Equations, 2010 We consider the classical Poincare problem $$ frac{dx}{dt}=-y-p(x,y),quad frac{dy}{dt}=x+q(x,y) $$ where $p,q$ are homogeneous polynomials of degree $n geq 2$.
Gary R. Nicklason
doaj
Results in PhysicsThis document elaborates on a newly introduced analytical method known as the “Variable Coefficient Generalized Abel Equation Method,” as proposed by Hashemi in Hashemi (2024), designed specifically for addressing the two-mode Cahn–Allen equation ...
Mir Sajjad Hashemi +3 more
doaj +1 more source