459 research outputs found
Solutions of time-dependent Emden–Fowler type equations by homotopy-perturbation method
In this Letter, we apply the homotopy-perturbation method (HPM) to obtain approximate analytical solutions of the time-dependent Emden–
Fowler type equations. We also present a reliable new algorithm based on HPM to overcome the difficulty of the singular point at x = 0. The
analysis is accompanied by some linear and nonlinear time-dependent singular initial value problems. The results prove that HPM is very effective
and simple
Existence of periodic orbits in nonlinear oscillators of Emden-Fowler form
The nonlinear pseudo-oscillator recently tackled by Gadella and Lara is
mapped to an Emden-Fowler (EF) equation that is written as an autonomous
two-dimensional ODE system for which we provide the phase-space analysis and
the parametric solution. Through an invariant transformation we find periodic
solutions to a certain class of EF equations that pass an integrability
condition. We show that this condition is necessary to have periodic solutions
and via the ODE analysis we also find the sufficient condition for periodic
orbits. EF equations that do not pass integrability conditions can be made
integrable via an invariant transformation which also allows us to construct
periodic solutions to them. Two other nonlinear equations, a zero-frequency
Ermakov equation and a positive power Emden-Fowler equation are discussed in
the same contextComment: 13 pages, 5 figures, title changed and content extended, version
accepted at Phys. Lett.
An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method
In this paper we propose a collocation method for solving some well-known
classes of Lane-Emden type equations which are nonlinear ordinary differential
equations on the semi-infinite domain. They are categorized as singular initial
value problems. The proposed approach is based on a Hermite function
collocation (HFC) method. To illustrate the reliability of the method, some
special cases of the equations are solved as test examples. The new method
reduces the solution of a problem to the solution of a system of algebraic
equations. Hermite functions have prefect properties that make them useful to
achieve this goal. We compare the present work with some well-known results and
show that the new method is efficient and applicable.Comment: 34 pages, 13 figures, Published in "Computer Physics Communications
Symmetry, singularities and integrability in complex dynamics III: approximate symmetries and invariants
The different natures of approximate symmetries and their corresponding first
integrals/invariants are delineated in the contexts of both Lie symmetries of
ordinary differential equations and Noether symmetries of the Action Integral.
Particular note is taken of the effect of taking higher orders of the
perturbation parameter. Approximate symmetries of approximate first
integrals/invariants and the problems of calculating them using the Lie method
are considered
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